Life is a Test: A Series of Pony Logic Puzzles

Chapters

Trixie's Rehearsal Woes
The Answer 2
Gambling Is Not A Sin, Provided That You Always Win
The Answer 3
First One Guy Makes A Bridge...
The Answer 4
Fatal And May Even Cause Death
The Answer 5
Way Too Much Work To Escape
The Answer 7
The Answer 8
Says It All About Diamond Dogs Really
The Answer 9
Flim and Flam Are Just The Worst
The Answer 10
Hello Darkness My Not-All-That Old (But I Guess It's Relative) Friend
You Knew I Had To Fall Back On One Of The Really Well-Known Ones Eventually
It's A Cake, But It's Also A Time-Waster
The Answer 13
Hello There, I Want To Play A Game...
The Answer 14
The Answer 15
The Friendship Games Has Too Much Money
The Answer 16
Nice Ponies Finish Last
A Game That's HARDER The Smarter You Are
The Answer 18
Surprise WITHIN A Surprise? Surprise-ption
Music Is Subjective, But Come On
The Answer 20
Hogwarts Doesn't Offer Maths
The Answer 21
The Answer 22
You Probably Would Have Preferred To Play Consequences, Really
The Answer 23
Don't Think It Counts As Fine Print If The Print's All The Same Size
The Answer 24
Fastest Fillies First (And Second And Third)
Slower Is The New Faster
Cutie Mark Crusader Engineers
The Answer 27
I Needed A One-Off Character From The Comics For This
The Answer 28
S.P.L.A.T (Society of Ponies Leaping from Alpaca Towers)
The Answer 29
Curses!
Another Will To Sort Through
The Answer 31
Those Who Want Money And Those Who Want A Bit More Money
Why Do So Many Puzzles Involve Being Imprisoned Somewhere?
The Answer 33
It Was Such A Lovely Day, Too
The Answer 34
Fssssssssssssssssssssssssssssh
It Got Worse
Rock, Rock, Rock (No Fingers, Genius)
The Culmination Of All, Part 1
The Answer 38
The Culmination Of All, Part 2
The Answer 39
The Answer 6
The Poison Apple Joke Cider
The Answer 1
If You Don't Like Broccoli And Hazelnut Cupcakes, Tirek Wins
The Art Of Business (And Unlikely Logic)
The Answer 11
The Answer 12
Mo' Money, Mo' Rocks, Maud Pie
The Answer 17
The Answer 19
Is It Called A Bucket Because That's What Ponies Say After Rage-Quitting?
The Answer 25
The Answer 26
The Answer 30
The Answer 32
The Answer 35
The Answer 36
The Answer 37

Trixie's Rehearsal Woes

Greetings, loyal readers! It is I, the Great and Powerful Trixie!

What's that? You've never heard of me? Don't you lie, I see you, wasting your time on this website when you could be working! Look at Trixie! Trixie is ALWAYS working!

Ahem.

Anyway, I have been asked to impart a certain tale of woe that could perhaps be used as an invaluable learning experience to lost lambs such as yourselves. No, don't stop to thank Trixie or anything, it was nothing. Well, the disaster was something to Trixie, but unexamined lives and all that.

Well, I had recently come up with an act so great it would surely require a level of technological sophistication not unlike that of the most well-known princess crowning ceremonies. Oh it was marvelous! It would have been a great pyrotechnic marvel of explosions, fire, exploding fire and so many fireworks and illusions that Trixie would be a superstar overnight. And by that I mean MORE of a superstar, because that's what Trixie is already. Yes.

But the last thing I wanted was to have the press shove their cameras and their notebooks into Trixie's business, so I hatched a plan. A scheme of sorts, if you will. I had a crew of thirty ponies all ready, all being very well paid by Canterlot sponsors, and so I decided to split them into three groups to rehearse the act independently.

Now, never let anypony say that Trixie ever lets an act go stale! No sir! So Trixie decided to keep them on everypony's toes, even during practice. I told them that they wouldn't know which teams they would be assigned to, and had them sorted out with certain...instructions.

What's that? Why didn't Trixie just go the simple route for an act as big as this? Because Trixie ALWAYS remains consistent on how stagehands are arranged, and Trixie wasn't about to stop now!

Yes, I realise that it was a terrible idea NOW, thank you. Now may Trixie FINISH her unfortunate comedy of errors? As I was saying...

Each of the thirty ponies would turn up at the Canterlot train station at random times during the day, and they'd get on the first train departing to either Las Pegasus, Manehatten or San Diegoat. Now, Trixie did check the timetables, and it so happened that there were an equal amount of trains bound to each destination, so it stood to reason that Trixie should have a decently even split of teams, each one ready to rehearse their individual parts for Trixie's grand performance.

But alas! Upon returning to Canterlot to coordinate the operation, Trixie discovered that the plan, the beautiful operation, had hit a snag! I had received word that out of the thirty ponies that were part of this glorious undertaking, TWENTY FIVE of them had arrived in Las Pegasus, and only a measly THREE ponies were in Manehatten, while the remaining TWO were in San Diegoat!

Now as you can imagine, Trixie was considerably hacked off by this! Oh there were a lot of angry words exchanged, but each and every pony involved swore on Princess Celestia that they didn't disobey Trixie's instructions. Hmph. Personally Trixie believes that the bright lights and glitz of Las Pegasus were too much of a siren's call for these cretins.

But since I was told that there was a perfectly reasonable explanation for it (it was some nerd in glasses who said he worked on 'fanfiction', whatever that is), Trixie wants to hear it from you. Yes, you. Don't tell me you can't explain to Trixie why my glorious act was nearly ruined by a snag that Trixie had not foreseen!

Author's Note

So that's your puzzle. For those who zoned out of Trixie's rambling, here's the summary:

Three destinations: Las Pegasus, Manehatten and San Diegoat.
There's an equal amount of trains to each destination.
Thirty ponies turn up at random times during the day.
Said ponies catch the first train going to one of these destinations.
The result is 25 ponies in Las Pegasus, 3 in Manehatten and 2 in San Diegoat.
Nopony disobeyed instructions.

PUZZLE: Figure out how this could have happened.

The Answer 2

Although each pony arrived at different times, the train departure times were all fixed, and not evenly spaced out either.

You would expect a reasonably even number if each train departures were all evenly spaced out. But they weren't, and Trixie didn't think about this.

Imagine a scenario where there was only one train to each destination per day. For example, one Las Pegasus train was at 10:00, a San Diegoat train was at 11:36 and a Manehatten train was at 14:00. If you arrived between 14:00 and 10:00 THE FOLLOWING DAY, it means that the first train to catch would be the one going to Las Pegasus at 10:00.

So there'd be a 20/24 chance of going to Las Pegasus (hence why 25 ponies wound up there), a 3/30 chance of going to Manehatten, and a 2/30 chance of going to San Diegoat.

Gambling Is Not A Sin, Provided That You Always Win

The School of Friendship: originally a plan conceived by Princess Twilight Sparkle to spread friendship beyond Equestria, it fought through bureaucratic interference, a tiny budget and somewhat cheap hiring standards to become the best (if only because it was sort of the only) facility for relationship education the world of Equestria had ever seen.

Despite its shaky start however, it had grown to be a well-loved place for students of all species to learn about friendship. After several months at it, they had found a rhythm of sorts, and as long as the students didn't realise the teachers were just sort of making it up as they went along, whatever worked, worked. It was on one such day that Twilight, the head teacher, came to one of the classrooms with an important announcement.

"A field trip?" asked Gallus. The young griffon looked up from preening his blue feathers momentarily,

"That's right!" Twilight smiled. "Rarity oh so generously agreed to organise one for you students! After the last one, you all agreed that the last one with Applejack and Rainbow Dash was a success...somehow..." Twilight's eye twitched slightly, for reasons that escaped the students in the classroom. "...so I thought we could organise another one!"

"Wait, I thought Pinkie Pie was organising one for today too," Smolder pointed out, raising her clawed hand.

"Well, there's that, yes," Twilight nodded. "It's to the snowy mountains of outer Yakyakistan."

"Thought so," Smolder shrugged. "That's why I packed something warm. You know, duh, still a reptile."

"So, what?" Cozy Glow raised an eyebrow. "Are half of us going on one, and the other half goes on the other?"

"Essentially. But since I know some of you already have an ideal spot in mind, so to ensure it's fair for everyone here...we're going to have it decided randomly!"

Cozy Glow hid a smirk across her face. What no-one in the class had realised however, was that she already knew this would happen. She happened to stumble upon the lesson plan as she was about to head home yesterday, and seeing that the head office door was open, what else was a curious filly to do but look around?

Yesterday afternoon...

It didn't take long to find the lesson plan on Twilight's desk. looking it over, she saw that the field trips was going to be decided via a draw over who got to go on which trip. One to the forests in the deer's territory, and the other in the freezing mountains of Yakyakistan.

And as much as Cozy Glow was a decent skier, she decided the lure of more friends on a more close and personal orienteering trip was a better outcome. And the cold generally stank, anyway.

She looked at the plan. They would be assigned a trip based on drawing stones from one of two random jars. Whoever picked a blue stone went to freeze their flanks off in Yakyakistan. Those who got a red stone were heading to the forests. Each jar would have six stones each, one containing only red, the other only blue. Each student would be blindfolded and made to choose one of the jars, which would be hidden under a blanket. Once they chose a jar, they'd fish one of the stones out.

Fortunately Cozy Glow was blessed with some degree of cunning, and she soon realised that there was a way to cheat.

She considered her options in her head the next morning: the morning of the trip. She was pretty sure she could sweet-talk the students into letting her be the first to pick, but the main problem was the frankly unfavourable odds. After all, there were six blue stones and six red stones to pick...

She briefly excused herself for a bathroom break, and quickly made her way to Twilight's office again. When she walked into the empty room for the second time, sure enough, there were the jars under the blanket, ready for the draw.

She glanced up at the clock. Only a one minute before Twilight showed up for the test. Sweating, took the jars from under the blanket, moved the stones around to best suit her odds, and promptly dived for a good hiding place as she heard the keys jangling around at the lock outside...

Author's Note

So. What would you do if YOU were Cozy Glow? Here's the basic summary:

There are two jars.
One jar contains six red stones, the other contains six blue stones.
You select a jar at random.
You then pull a stone from that jar, also at random.
You cannot dispose of any of the stones.

PUZZLE: How can you rearrange these stones to maximise the odds of pulling a red stone?

The Answer 3

Remove all except one of the stones from the red jar and put them in the other jar.

If you choose the jar with the one red stone, you're now guaranteed to get a red one.

Odds of picking the jar with the one red stone: 50% (1/2)

If you choose the other jar, there's a 5/11 chance of picking one of the red stones from it.

Odds of picking that jar (1/2) x Odds of picking red stone from said jar (5/11) = 5/22 (approx 23%)

So adding the 2 probabilities, Cozy now has an about 73% chance of choosing a red stone.

First One Guy Makes A Bridge...

"Thank you SO much!" exclaimed the Alpaca King. "You have managed to thwart the uprising of the giant gingerbread spiders AND restored the sacred softball of righteousness to its rightful place: atop the throne of Great Justice!"

"Ah have no idea how we even did that," Applejack shook her head in exhaustion. There were bags under her eyes and her mane looked as though it hadn't been brushed in a week. It was still also resolutely blue: the sap hadn't washed out yet.

Pinkie shrugged. She looked just the same as ever, apart from the eyepatch over the left eye. "Neither do I. We started this chapter on the aftermath. Not even I know how we pulled it all off."

"Maybe somepony will write it down one day," Spike suggested.

"Or maybe we will never speak of it again," growled Rarity, as she continued to pull the leaves and twigs out of her mane.

"Eh, that too."

"But..." continued the Alpaca King, "...I AM going to have to pin the whole bread roll poisoning on somepony...and so, I'm going to have to rather conspicuously chase you out of town now. I do hope you understand."

"Wait, what about that whole lesson in friendship thing? You know, THAT!?" Applejack exclaimed.

"Well, nothing like a common enemy to put petty differences aside. How about that one? Now then, please get them, if you would," said the Alpaca King, motioning to the guards. "I do hope you all enjoy the exercise."

"AJ, grab the diamonds and run!" Pinkie grabbed Spike and pelted out of the hall.

"Oh sure, leave the heavy lifting to the exhausted pony. That'll go well," grumbled Applejack, as she hauled the sack onto her shoulder.

"Leave it, it's not worth it!" shouted Rarity.

"Actually," pointed out the Alpaca King, "I'm willing to give each of you a fifteen minute head-start as a courtesy. So it's actually totally worth it."

Rarity paused. "Oh...well, that's very courteous of you. Thank you." She then watched Applejack finish getting the bag over her shoulder before slinging her front hoof over to support her friend. "This changes nothing!" she shouted as they both hobbled out.

The group of four were chased away from the stronghold that was the Alpaca Village for quite a distance, with the pursuit never relenting, not even until nightfall, and then they had to light the last torch they brought with them. By Rarity's best estimate, the pursuers were still at least fifteen minutes behind, judging by the lights of the torches she could make out behind her.

"There's the bridge! Up ahead!" shouted Pinkie, pointing the torch left. "C'mon slowpokes!"

"Oh thank Celestia, my shoulders are killing me. Even more," Applejack sighed. the four gathered together at the start of the swaying, wooden bridge. It was directly over a 2,000 foot drop (as the signs on both sides liked to cheerfully announce to tourists), which meant one misstep and an unfortunate victim would wind up flatter than Sugarcube Corner's sweet crepes.

"It's so dark," Spike narrowed his eyes. "I can't even make out what's in front of me without the torch."

"Well, that's clearly not a problem for our pursuers, evidently," Rarity huffed. "The good news is we should be at least 17 minutes ahead of them..."

"How'd you figure?" asked Applejack.

"Heavy armor. It weighs them down. But that's beside the point." She turned to the group. "Does everypony think they can get across in time?"

"Just give me a minute!" Pinkie replied happily. "...I'm being literal here. It really is exactly a minute. I counted the first time we crossed this."

"Eh, I'm not as fast, but still pretty fast. I mean, for someone who's only got little legs," Spike answered. "I can't take your giant strides, but I'd probably catch up to Pinkie in a minute, though."

"I'd need a few moments to keep my nerves," Rarity admitted.

"C'mon, Rares! We don't have time for a fear of heights now!" Applejack was now watching the growing sea of lit torches and the faint shouts of the mob in the distance.

"Not heights, FALLING, darling. And I didn't say I wouldn't cross. But I'd need five minutes."

"Well, Ah've still got this sack of gems over mah shoulder," Applejack motioned to the brown burlap bag. "Ah'd need what, eight minutes to get across, tops."

"Well, then that just leaves plenty of time to cut off the bridge once we're all across and lose the mob, so what's the problem?" Spike asked.

"That," said Pinkie, pointing to a small wooden sign right at the start of the bridge. The group huddled round. Rarity raised the torch, and there in the light of the flames, it read:

WARNING: NO MORE THAN 2 AT A TIME WHEN CROSSING

"Oh yeah," Spike gulped. "Forgot about that."

"...and thus as always, fate conspires to make everypony involved unnecessarily exercise the frontal lobes as well as the muscles. Because it always does," Rarity sighed. "So, how are we doing this then? We've only got fifteen minutes before the mob catches us..."

Author's Note

What a stumper. Okay, so here's what you're working with here:

It's not possible to cross the bridge without a torch.
The bridge can only support the weight of two individuals at a time.
There is only one torch to go round.
Each one takes different times to cross the bridge:

Pinkie: one minute
Spike: two minutes
Rarity: five minutes
Applejack: eight minutes

PUZZLE: How can everypony (and Spike) get across the bridge in only fifteen minutes?

The Answer 4

Note that a group is only as fast as its slowest member. The solution therefore is:

Pinkie and Spike both cross the bridge (2 minutes)
Pinkie runs back to the other side with the torch (3 minutes)
Applejack and Rarity cross together (11 minutes)
The torch is passed to Spike, who runs back to Pinkie (13 minutes)
Pinkie and Spike cross again (15 minutes exactly)

Incidentally, it was only when everypony was across that Spike remembered that he was a dragon, and therefore pretty much was a walking talking torch. Everypony gave him the cold shoulder for the rest of the trip back to Ponyville.

Fatal And May Even Cause Death

Ponyville may have had a few problems, regular invasions from evil forces notwithstanding, but Ponyville General Hospital certainly wasn't one of them. It was where any sick pony, young or old, could visit and be patched up by some of the finest staff around town. From broken bones to a bad case of the trots (although some of the ridiculously obscure diseases were left to the zebra on the outskirts of town).

It was on one such day that a nurse, who had finished her rounds for the day, found herself chatting to two friends of hers, a smart looking brown stallion in a bowtie, and a grey pegasus with a wonky eye.

"...and that's when I said, 'But out of context conversations are the best part!'" Time Turner said with a grin.

"Well, obviously. Low effort punchlines are just so easy..."

The conversation was suddenly interrupted by Derpy's face turning a slight green colour, followed by the grey mare starting to sway on her hooves.

"Miss Hooves!" gasped Nurse Redheart.

"Ah, yes," Time Turner's grin faded. "I did expect her to come down with something. Especially after the Space Mines..."

"What?"

"Don't ask." Time Turner reached into his bowtie and pulled out two glass jars, both containing what appeared to be small white pills. "Gotta love the bowtie. Bigger on the inside. Anyway, I know what this is, and I've got the medicine for it."

"Seriously?" Derpy croaked out. "Gimme." And she reached her grey hooves out and swiped the jars from Time Turner. "Oi!" he protested.

Derpy then poured out two pills from the AR jar and one from the AS jar, and with considerable effort, raised the pills to her mouth...before collapsing to the floor with a somewhat darker green look across her face.

"Okay...well, this hurts about six fourteenths as much as I thought it would..."

"Oh goodness..." Nurse Redheart said with grim determination. "I suppose I'll have to administer it then."

She picked up the pills. "Okay..." Nurse Redheart looked down at the medicine in her hoof. "So I give the patient all three of these pills in her hoof then?"

"All THREE?"

"Well, yes? There's three pills here."

"Wait, let me see..." Time Turner stared at Nurse Redheart's outstretched hoof. Sure enough, there were three identical looking pills lying there. "Horseapples."

"What's the problem?" she asked. "Not the right dosage?"

"MMmmmmmm...sort of." Time Turner said nervously. "See...one pill is AR and one pill is AS. Two different meds that work together and need to be taken at once to counter the poison. Except they both look the same. Same size, same colour, weight, smell, IQ, ATM number, dental records and favourite food."

"Out of EVERY zenith of sheer improbability WHY!?" Nurse Redheart shrieked.

"Very poor communication between staff apparently."

"What happens if the dose is incorrect?" Nurse Redheart was almost dreading the answer.

"Well, then Derpy joins the great open meadow in the sky. Instantly." Time Turner nodded. "Almost instant anyway. Fascinating really."

"What sort of idiot would make medicine that can kill a pony?"

"Every medicine in high enough doses can. Not difficult," Time Turner replied, rather dryly.

"Um...Doc?" Derpy weakly raised a hoof. "Still poisoned here."

"Yes, I know dear, we're trying to figure out how to solve this little dilemma." Time Turner rubbed his chin with his hoof.

"There's an extra AR pill in there if it helps..."

"FOR CELESTIA'S SAKE!" Nurse Redheart threw up her hooves in exasperation. "Can't you just throw these ones away and get two new ones?"

"But what if we need them later?" Time Turner pointed out.

"What are the odds it WOULD happen again?"

"What are the odds two independent chemists would make two identical looking pills down to even the little red stripe across each one? It would be the absolute zenith of sheer improbability, but it happened anyway."

"Forget this! Let me just give her the right medicine..."

"Fine. We play it your way. But I still say we could do this the most efficient way..."

"I can't believe I'm going to croak...because of a logical...problem..." Derpy weakly groaned out.

Author's Note

Well. What are the odds? High, if the winds of drama are in your favour. Anyway, here's what you must work with:

Two types of pills, AR and AS, that are indistinguishable from each other.
One of each pill is needed to cure Derpy.
Derpy messes up and adds one more AR pill to the pile, making three pills.

PUZZLE: How can Derpy take the correct dosage of each pill without wasting any other pills?

The Answer 5

Add another AS pill to the pile, then grind the pills into a powder.

All Derpy has to do after that is take half of the mixture and save the other half for the next time she gets poisoned.

Add another AS pill to the pile, then cut all the pills in half and divide them into 2 piles. (Make sure you have one half of the AS pill you added in each pile)

Derpy can then take one of the pill piles and save the other half for next time. You might think this is problematic since the pills are indistinguishable, but now you've added another AS pill it doesn't make a difference. While she's talking the first half she will always have the equivalent of one AR and one AS pill.

"NEXT TIME!?"

Way Too Much Work To Escape

Often, Daring Do, archeologist extraordinaire, wondered how she found herself in situations like these.

Oh, it was easy enough once she was back at her writer's desk penning the aftermath of her last great adventure, but while it was still HAPPENING, it all seemed somewhat of a blur.

It was so routine. She had heard of the legendary Skull of Agesand, and having ridiculously itchy feet and a thirst for adventure (and money) she set off to find it. Unfortunately, for reasons that she would eventually have to sort out in her head once it was all done, she had stumbled into some sort of magic-based trap created by her nemesis, Ahuizotl. Well, enemy, nemesis, it really depended on how involved he got and what he was doing during daring's escapades.

So, this was just another adventure, really. So far nothing unexpected. Even if the trap was somewhat of an annoyance: she was right under a circular dome made of purple magic that covered the air above her. She recognised the magic well enough to know she could probably walk out of the sigil if she tried, but she knew Ahuizotl wouldn't leave her without a guard.

It would be sort of romantic to let her assistant Herpy rescue her, she thought, but she never liked stereotypes.

"...so, gremlin," Ahuizotl's talk with a small red demon from Tartarus he bound to his service shook daring out of her musing. "I have every confidence you'll be fast enough to catch her should she try to escape, as long as you don't enter the magical sigil..."

Daring tried to get herself airborne, beating her wings as furiously as she could, but soon found that her wings felt...heavy for some reason. After a few seconds, she was panting rather deeply out of exhaustion.

"Oh, don't try beating those wings now, my dear. The gravity's increased in that space. You'll just get tired." Ahuizotl shook his head. "Did you think I WOULDN'T think of that?"

"Honestly, sort of, yeah," Daring admitted. "Worth a try, though."

"Unlike that glorious relic, which will be worth so much more than a mere 'try'," Ahuizotl grinned. He turned to the gremlin, and adopted a considerably more serious face. "Make sure she doesn't leave that sigil. Fortunately the magic involved is so thorough not even you could screw this up, but you know me: I'm saying this just to make sure you're better. By any means necessary. Are we CLEAR?"

"C-crystal." The gremlin looked nervous. Daring had to admit she felt a bit sorry for the small demon: no-one ever deserved to have to play intern to anyone like Ahuizotl. She supposed even he could make actual creatures from Tartarus wet themselves.

"Excellent," Ahuizotl grinned all to malevolently. "Now if everyone will excuse me,I have a tomb to plunder." And he walked off, cackling to himself in the distance.

"Geez. I get it, you're evil. Seriously, you're just missing the moustache to twirl."

Daring allowed herself a small smile. "Oh great, now I can't get the image out of my head." However, as amusing as the thought of her arch-nemesis adopting and even more stereotypical look was, she had a trap to escape from.

Daring started to gallop towards the edge of the sigil as best she could with the increased gravity, but she soon found the gremlin, with a wicked grin on his face, right at the end of the edge. So she turned around and headed back to another, but that was to no avail as well.

Realising that the sensible thing to do if she was going to escape the clutches of the infernal creature, she made her way back to the centre. By her estimates, she was moving four times slower running than the gremlin could fly around the sigil.

Once she was out, however, the magic paralyzing her wings would wear off, and she could fly: a much faster means of travel than galloping. She wasn't as fast as her rabid fan Rainbow Dash at Daring-Con, but she wasn't a slowpoke.

Actually leaving was the tricky part, though. But there was truly no inescapable trap, in her knowledge. there would be a contrived coincidence or flaw that would allow her to get free (even if her readers would call it a flank-pull when the adventure actually hit the pages). So she sat at the centre of the sigil, and began to scratch what she knew so far on the floor with her hooves...

Rather astonishingly, despite having seemingly covered all the bases, by the time Ahuizotl returned, all that was left was a rather frightened looking gremlin and a rather pointedly archeologist-free magic sigil. The news, as one can imagine, didn't sit well with him.

"WHAT DO YOU MEAN SHE ESCAPED!?" Ahuizotl roared.

"S-sir! I swear on my demonic existence that it wasn't my fault!" stammered the gremlin.

Unfortunately, he couldn't, and the gremlin was dismissed. Painfully. Not even his ability to go from zero to top speed could save him from the wrath of Ahuizotl.

Author's Note

Well, he couldn't. But you may be able to.

Daring Do is in the centre of a circular magic sigil 30m in diameter.
The gremlin guard patrolling the sigil can move four times faster than Daring can while she's contained within it.
Once Daring is out of the sigil the gremlin cannot catch her.
The gremlin tracks Daring by heading towards the edge of the sigil that Daring is approaching.
For simplicity's sake the value of pi is 3.14.

PUZZLE: How did Daring manage to escape from the magic sigil?

The Answer 7

Start both hourglasses at the same time. By the time 5 minutes pass and the 5-min hourglass is up, 3 minutes are left in the 8-min hourglass. (5 minutes)
The moment that happens, turn the 5-min hourglass upside down. Wait another 3 minutes for the 8-min hourglass to run out. By this point 3 minutes worth of sand will have collected at the bottom of the 5-min hourglass. (8 minutes)
Turn the 5-min hourglass back over again and wait for the last 3 minutes. (11 minutes)

The Answer 8

You know wherever the three breaks in the chain are, you have three single broken links. Those will at least take care of your first three payments.

Continuing the thought experiment, you realise that you'll need a length of chain four links long to make a fourth payment, since you're only allowed three breaks. So snap the fifth link in the chain.

With that four-link chain and the three single links, those cover up to the seventh payment. Now, when the time comes to make an eighth payment, you need an eight-link chain, taking back the first seven links. So you snap the ninth link of your now fifty-eight link chain.

You've now used up fifteen links so far, so when the time comes to make a sixteenth payment...you guessed it. Snap the seventeenth link of your now forty-nine link chain.

That now leaves you with three single broken links, a four-link chain, an eight-link one, a sixteen-link one and a thirty-two link one. From there, you just keep swapping the links backwards and forwards as needed to keep the payments up.

Says It All About Diamond Dogs Really

At the heart of the throne room in Princess Twilight Sparkle's Castle, there is the Cutie Map: a holographic image of a map created by the six gemstones embedded in the thrones of her friends.

With magic not even Twilight could fully understand, it seemed to be able to detect places where there was unrest: friendship-related problems to solve, if you will, and it would assign one or more of the six friends to go to wherever the map glowed and solve that problem. For other reasons Twilight couldn't understand either,it was never to solve the problem before it happened, just in time to stop a village catching on fire, or while things escalated to a potential feud.

They were never given anything simple. Certainly not anything so simple it couldn't possibly be screwed up.

It was on one such morning that Rarity and Rainbow Dash had been called to the throne room. They knew when they were needed as their cutie marks would always glow at the same time as the map's chosen.

Rainbow Dash and Rarity both stared at the glowing Cutie Map with interest. "This one's pretty close to home," Rainbow remarked.

"Indeed," Rarity nodded. "If I'm not mistaken, it's glowing around the area of the quarry I regularly visit to obtain more gems."

"The same one where you got mare-napped?" Rainbow asked. "Except not really?"

"Looks like it," Twilight turned to the pair. "Still, it doesn't matter where the cutie map indicated, a friendship problem is a friendship problem. And it falls to you to see it solved!"

"Oh, I suppose so," Rarity sighed. "We help everybody, yes? Still, if it has anything to do with those absolute ruffians known as the Diamond Dogs, rest assured I will have a few choice words to say to them when we meet again!"

"C'mon, Rarity," Rainbow raised an eyebrow. "Maybe they won't be the same Diamond Dogs. Maybe those three were just jerks even for them. It would take a really stupid coincidence for it to be them again..."

"AAAAAAAAARGH! It's YOU! WHY ARE YOU HERE, SHE-DEMON!?"

Rarity stared at the panicking Diamond Dog Rarity vaguely remembered being called 'Rover'. "Well, Rainbow, it's been one contrived coincidence after another for us lately."

"Yeah..." Rainbow stared, amazed. Rarity's marenapping was some years ago, but it would seem even the less-than-intelligent Diamond Dogs could at least remember what they considered important. "Guess a warm welcome's out."

"Yes. Although admittedly, that reaction DOES put a smile on my face," Rarity smirked. She took a sharp breath, mentally preparing herself for the grime and dampness of the caves. "Well, might as well see what they want, I suppose."

The pair made their way down into the darkness. Rainbow soon found herself feeling uncomfortable. The caves barely afforded any room to fly, and she could feel droplets of water occasionally hitting her back. It was also not very well-lit, but at least she could see Rarity in front of her. Rarity, meanwhile, had elected to wear a fashionable white raincoat into the caves, complete with a lantern. She'd offered the same to Rainbow, but she blew it off, saying it couldn't be as Rarity sounded.

She was now starting to at least want a raincoat now.

"NO SHARING!"

A loud voice at the end of the tunnel Rainbow and Rarity were traversing rung out. Quickly, the pair trotted to the light at the end, and were greeting by a frankly overwhelming sight.

There, in the centre of the large cavern. was an enormous pile of diamonds, reaching up to the ceiling. On top of that was what appeared to be some sort of throne, with a brown and rather unkempt-looking Diamond Dog sitting in what was an attempt at being regal. Rarity found the effect somewhat underwhelming. Surrounding the pile were several Diamond Dogs, two of whom Rarity recognised as her marenappers Fido and Spot (what another contrived coincidence), appearing to beg the Diamond Dog at the top of the pile for just one gem.

Spot turned to the pair. Spotting Rarity, instantly, his face went white. "AAAAAAAAARGH! It's YOU! WHY ARE YOU HERE, SHE-DEMON!?"

"Wow, this cave must have one heck of an echo," Rainbow dryly noted. "Look, we're not here for you. I don't think. We heard there was a problem and we came calling, that's all."

"Problem?" Fido trotted up to them. "Barky won't give us just one shiny gem! He just makes up dig them up and then won't give us any for all his hard work!"

"Fido!" shouted Spot, pulling Fido to one side. "Why are you talking to the white pony!? She's evil!"

"But Spot!" said Fido. "Maybe the white pony can make Barky give us just one gem. Her whining... and complaining...and screeching...if she could be turned..."

"I DO have other personality traits worth mentioning, you know!" Rarity protested from afar.

After a few minutes, they both finally agreed to give it a shot. "Okay, pony..."

"In case you curs have forgotten, it's MISS, Rarity, or Miss Rarity," she said without missing a beat.

"Miss Rarity," Spot said, at least having the good sense to look ashamed, "please make Barky give the rest of us Diamond Dogs just one shiny gem!"

"Well..." Rarity said, putting a hoof to her chin in thought, "...oh, go on, then. You DID say please, after all. Come, Rainbow."

The pair trotted up to the ridiculously tall pile of diamonds. Not wanting to suffer any neck strain talking up to Barky, Rainbow picked up Rarity and flew to the top.

Rainbow decided to get the train of conversation rolling first. "Uh, excuse me, dude, but it sounds like these guys down there could be spared a gem or two..."

"NO SHARING!" shouted Barky.

"And why not?" protested Rarity.

"Sharing stupid." Barky nodded. "They want equal pay, but this pile can't be shared equally. Ever."

"What do you mean, they couldn't be shared equally?" Rainbow asked.

"Ten Diamond dogs dug these diamonds up," Barky explained. "But when we tried to share them equal, we were one diamond short. Dog with one diamond short attacked Barky, so Barky banished him from caves.

"The next day we tried dividing diamonds into nine. But we were still a diamond short. Dog with one diamond short attacked Barky, so Barky banished him from caves.

"The next day we tried dividing diamonds into eight. But we were still a diamond short. Dog with one diamond short attacked Barky, so Barky banished him from caves.

"The next day we tried dividing diamonds into seven. But we were still a diamond short. Dog with one diamond short attacked Barky..."

"...So you banished him from the caves, right?" Rainbow asked. Barky nodded. "Are you serious?" Rainbow's mouth hung open, amazed at how all the dogs involved could be so unbelievably stupid. "Did the rest of them just not get it? At ALL?"

"To be fair, it is keeping entirely with what I remember about Diamond Dogs," Rarity said dryly.

Rarity and Rainbow continued to listen to Barky's story with increasing amazement and incredulousness of the sheer idiocy of Diamond Dogs, until finally...

"...The next day we tried dividing diamonds into two. But we were still a diamond short. Dog with one diamond short attacked Barky, so Barky banished him from caves. And now only Barky has all the diamonds. That's why NO SHARING! Sharing dumb. Doesn't work."

While the tale was being spun, Rarity was already crunching several numbers in her head in an attempt to drown out the gravelly and frankly grating voice of the Diamond Dog king. She was no closer to devising a resolution to this friendship problem, if one could call it that. But she did at least know how many gems there were in the large pile Barky was sitting on.

Author's Note

I really need to up my internet searching because seriously, I got so many involving maths its stupid.

You have a pile of diamonds.
When one tries to divide the diamonds into even piles of ten or less, it will always be one diamond short.

PUZZLE: What is the lowest number of diamonds in the pile?

The Answer 9

There are 2519 diamonds.

You're basically looking for the lowest common multiple of 2 to 10, and then minusing 1 because Barky always found himself one diamond short.

Flim and Flam Are Just The Worst

Oh, hello there, stranger! He's Flim, I'm Flam, and we're the world-famous Flim Flam Brothers!

Oh? Where IS Flim, you ask? Oh, not to worry, my brother is simply plotting our escape route-uh, I mean, scouting the road ahead. We are travelling salesponies, as you can see. Can't stay too long!

Oh, no, by all means, take your time browsing! Everything is very reasonably priced, I think you'll find!

Mmm? Ah, I see you have a fine eye, my friend! You see, we happened to obtain this from the village not far behind us, in fact. Along with all of their bits.

Oh? Well, we happened to come across it during our travels and we've been regular visitors to the place ever since! It's just so PROFITABLE, you know? Not an overly friendly place I will admit, but a good salespony knows how to sell ice to a polar bear and make it come back for more! I swear it has nothing to do with the fact we got lost in the desert with no water and our loud attempts at a rain dance made them pity us and take us to their village.

You see, that village is rather...quaint. It follows a set of rules that everypony in the village must obey. First, we...aren't entirely welcome in that place. They believe in sustaining themselves on the bounties of the earth and won't accept buying from outsiders like us.

Ah, how then have we managed to make any sales there, you ask? Well, we disguise ourselves as simple tourists, and know how to be discrete if we must, and all the stallions in the village know where to find us when we visit. Yes, all eighty of them. I mean, goodness knows what all eighty of their wives must think.

Speaking of wives, the second rule is that all the stallions in the village answer only to their wives, and if they discover their husband broke any of the village's rules, they are to be banished to Tartarus. With extreme prejudice. The zebra mares there are pretty hardcore about it AND their magic, I must say.

...Ah, I know why you have such an incredulous look on your face. How then is it still standing, this village? Well, my brother and I discovered when we first visited that all the mares know what everypony in the village is up to...EXCEPT for their own husbands. I know, what a shock! The only reason nopony has spoken up until now is the third and final rule: nopony in the village must interfere in the personal lives of the other villagers. Even the stallions follow this rule. Nice to have some integrity, at least.

Ah, you've decided on THAT one? Good, good! Eight bits, and do enjoy your gingerbread spider repellant!

...yes, it is a rather peculiar village isn't it? Still, it's one of our hottest selling spots. Ah, talking of which, we avoided a rather close shave after we left the village today. I'm ashamed of our loose lips, really. Accidentally said out loud at least one of the stallions there was buying from us every time we visit. In front of the whole village as we were leaving.

Oh no, no no, it's nothing to worry about! I told you before, all the mares know of at least one errant husband! We weren't telling them anything they didn't already know. So no harm, no foul, yes?

Ah Flim, you're back! How's the road up ahead? Good, Well then, let us be leaving then! I doubt anypony else apart from our fine customer here will come if we remain here, so off we must go! Farewell!

Author's Note

Well, since I think the last puzzle was a bit too easy, here's something slightly more challenging. Ever so slightly.

Eighty pony couples in the village.
All mares have perfect knowledge of everypony's activities except their own husbands.
Any mare who discovers their husband buys products from the Flim Flam brothers is to be banished to Tartarus the very same day.
Flim and Flam lets slip that there is at least one stallion who buys from them.
All the mares are completely logical. Um...to a point.

PUZZLE: What happened after Flim and Flam left the village?

The Answer 10

On the evening of the eightieth day, all the stallions got banished to Tartarus.

Let's simplify the situation to explain what's going on. If there was only one couple in the village and Flim and Flam leaked the secret, the mare knows by default it's her husband that they're talking about and thus banish them that day.

In the event there are two couples, Flim and Flam's leak surprises neither mare, as they both think that they are referring to the other wife's husband (they don't know their own is an offender too, remember). They both conclude that the other will work out their husband deals with Flim and Flam and banish him, since they needn't worry about their own. But a day passes...and nothing happens. And THIS is where it gets interesting.

Both mares then conclude the only reason that the other did nothing is because they know of at least one other lawbreaker in the village. And since the only possible candidate left is their own husband, both mares conclude that both their husbands are guilty and send them to Tartarus.

What if there were THREE couples? Well, as before, nothing happens on the first day as expected, but a second day passes and nothing happens either. All three mares originally thought the other mares only knew one offender each, so they expected banishments on the second day, but the lack of action on the second night means that they actually know more than two errant husbands. That therefore means there must be three villains total and thus on the third evening, the husbands are banished.

Continuing this train of logic, in the event of each wife knowing seventy-nine errant husbands, they expect banishments galore on the seventy-ninth day. But when that day passes without incident, to their dismay, they realise that all the stallions, including their husband, are sinners. And so, law abiding as they are, on the eightieth night all eighty stallions are sent for an appointment with Cerberus.

Hello Darkness My Not-All-That Old (But I Guess It's Relative) Friend

The Crystal Empire, despite its name, isn't actually ruled by an emperor or empress, not even by BOTH an emperor or empress. No, it is instead ruled by the benevolent Prince Shining Armor And Princess Cadance, and despite the remote location of the empire and their frankly precocious and near-incurably powerful daughter Flurry Heart, they manage to get by as rulers.

One day, however, reports from the Empire archivist reports that King Sombra, the less-than popular previous ruler of the Crystal Empire (who rather notably wasn't an emperor either, but names are just labels), left behind trace remnants of his dark magic in the chamber downstairs, and is growing at a frankly alarming rate. If left unchecked, it could leak out of the vents and spread across the Crystal Empire, corrupting all its citizens into mini-Sombra clones, and even negating the magic of the Crystal Heart, the gem used to protect the entire empire, bringing a new age of darkness and despair.

And you wonder why nopony liked King Sombra: evil corrupting magic and oppressive rule aside, at least crime was kept low.

Fortunately, as former captain of Canterlot's Royal Guard, Prince Shining Armor has never shied away from getting his hooves dirty for his citizens, and he volunteers to go to the underground and contain the menace. Throwing up his best dome shield to protect himself and carrying Princess Cadance's love in his heart, he ventures into the unknown.

As soon as he arrives at the entrance of Sombra's chambers, he opens up his map. According to the piece of parchment, the chamber is a series of rooms, perfectly arranged into a 4-room by 4-room square. Shining is currently at the entrance, which was the room on the top left of the grid, and the exit was at the most south-west room. Each and every room is connected by airlocks (never let anypony say that Sombra was not one to keep up with modern technology as it happened), and Sombra's evil has managed to leak into every room except the entrance.

Knowing that as the size of an explosion increases, the number of problems that it is incapable of solving quickly approaches zero, Shining reasons that with ENOUGH explosions, he should be able to solve the problem of purging Sombra's taint. As it so happens, he is carrying several grenades powered by the Crystal Heart's magic for such an occasion, and he therefore decides to destroy each contaminated room one at a time, visiting each corrupted room once and then destroying it before he leaves.

Unfortunately, there is a catch. Once his zest for explosions clears up, he begins to realise that once he visits a corrupted room, he absolutely cannot leave without destroying the room, lest Sombra's evil escape via the airlocks to the Crystal Empire outside and turn all its residents into toothy, black-coated, stereotypical villains. There's also a far more pressing problem in that none of the paths he's drawn up so far actually allow him to destroy all the corrupted rooms without missing at least one.

So, how can it be done? Princess Cadance has made it quite clear that Shining can't pull any Heroic Sacrifices blowing himself up just to rid the world of Sombra (hopefully for good this time, he keeps coming back), because martyrdom is for chumps, and TV Tropes has ruined enough lives as it is anyway. So how can Shining Armor fulfill his princely duty and still make it back to his loving wife, whole and unspoilt?

Author's Note

You have a 4x4 grid of rooms. The entrance is in the top left room, while the exit is in the bottom right room.
Shining Armor must enter through the entrance and leave through the exit.
All rooms except the entrance are contaminated with Sombra's dark magic.
Once Shining enters a contaminated room, he cannot leave it without first destroying it.
Destroyed rooms cannot be returned to.

PUZZLE: How can Shining Armor destroy ALL the contaminated rooms and not become corrupted by darkness?

You Knew I Had To Fall Back On One Of The Really Well-Known Ones Eventually

Daring stumbled out of the stone door, coughing. The Room of Fire was pretty good as far as traps were concerned: it had almost entirely singed her jacket and hat and her face was completely covered in ash, but she was alive for the most part. The Trial of the Body was not one to be overcome easily.

The pegasus slowly made her way towards the next stone door at the other end of the corridor. There she was greeted by what appeared to a sigil, with an outline where a hoof was apparently meant to go, judging by its shape. Gingerly, Daring raised her left hoof to the mark, and tapped it. Instantly, a purple light erupted from the floor, and a strange, ethereal shape began to form to the right of Daring Do, causing her to sharply back away in alarm. After about ten seconds, the purple glow began to fade, leaving behind a semi-transparent outline of what appeared to be a mountain goat, with fur as long as the lies of her enemy Ahuizotl, with a matching beard reaching all the way down to the floor and trailing for about three feet.

"I am the Ancient Goat," the spirit said. "You who seek the treasures within, you have escaped the room of fire so you are surely brave. But let us see if your wits are just as abundant. Let me be your test!"

Daring nodded, regaining her senses. No archeological adventure had any puzzle that she couldn't solve, or any trap that she couldn't avoid, so she was feeling pretty confident. The moment she accepted, a purple smoke appeared right under Daring's feet. She quickly stepped back, and instantly, a set of old fashioned weighing balances materialised in front of Daring, along with what appeared to be twelve bronze coins in one of its pans.

Daring's face grimaced. To be honest, she had recognised the puzzle on sight as soon as it appeared, and she had to confess herself disappointed. "I have here," the Ancient Goat intoned, "a set of twelve identical looking coins and-"

"Really?" Daring stared at the offending items in front of her. "The coins and scales puzzle? Here I was hoping an ancient and influential civilization would have a shred of originality..."

"It was a different time!" protested the Ancient Goat. "We had fewer logicians back then!"

Daring rolled her eyes. "Okay, fine. So I have to find the one coin that's different, right? Is the coin heavier or lighter than the others?"

"That is part of the puzzle," the Ancient Goat smiled. "You need to find that out yourself."

Daring paused. "Okay, credit where it's due, that's a bit trickier. And how many weighings am I allowed?"

"Three," the Ancient Goat replied. "I do advise you give it a good think, I should say. Take the wrong coin, and you will find all respiratory privileges...rescinded from the curse of my ancestors. Pass my test, and you will be allowed forth, to the Trial of the Heart!"

Daring nodded. Despite how thoroughly outdated the puzzle was as far as modern society was concerned, a puzzle was a puzzle, and she couldn't wait for Ahuizotl to start catching up to her. "Right, better get cracking then!"

Author's Note

So...there we have it. Not even 15 puzzles in and I had to resort to this. That's annoying.

Eleven identical coins.
The twelfth coin is of a different weight than the others.
You have a set of old-fashioned scales - the one with pans on both sides.
You're only allowed three weighings.

PUZZLE: How can Daring find the coin that's different from the other eleven?

It's A Cake, But It's Also A Time-Waster

Howdy there, friend! Your friendly neighborhood Pinkie Pie here! Welcome to Sugarcube Corner!

...oh HI! Yup, I've got your usual box of pecan muffins here! 12 bits please! Ta!

Oh...um... before you go...you're not busy are you? You aren't? Oh thank Celestia, you would NOT believe the doozy I've gotten myself into today!

Remember your last birthday? I made that cake for you specially? You do? Good, because I got a custom order in from this pony with a tall top hat, and since you helped with my hourglass sticky situation I figured since you're super-duper smart you could help me sort out the logistics? Because you can't spell 'logistics' without 'logic'! Kind of. I mean, you just stick the 'stic' in there - heh, stick the stic. I like stick. It's a funny word. Stick stick stick stick -

Oh yeah. Weeeeeeell...get this. I'm making this cake. It's made up of twenty-seven slices. All in the shape of a cube, because he wants it sliced for twenty-seven guests. That way you combine it to form one BIG cube. Thing is, I've also got three tubs of frosting: red, purple and green. And he says I need to decorate the cake with frosting in a way that, when you stick 'em together, it forms one big cube that's a solid red, or solid purple, or solid green. He said he wasn't fussed about how the cake could be rearranged, just that he can form a solid red, purple or green cube.

Eh? Well, he's really into puzzles. As in REALLY into puzzles. Couldn't resist leaving this one with me. Said he also wants to amuse the party guests with it.

...no, he didn't leave the design plans with me. That's kind of why I need you. Pleeeeeeeeeease? I'll give you half-price discount on your next box of muffins! And I'll let you share any leftover frosting with me!

You'll do it? Thankyouthankyouthankyou! So what should I do first?

Author's Note

So there you have it. Another crisis of confectionary to conquer.

Twenty-seven cubes of cake.
You must cover the faces with either red, purple or green frosting.
You cannot cover a face more than once.
The cubes must be rearranged so they can form a solid red, purple or green 3x3x3 cube.

PUZZLE: How should Pinkie decorate the collective cake?

The Answer 13

First, cover the 3x3x3 cube in red frosting, because you'll need that regardless.

Once you've taken the whole cake apart, what have we actually got?

Of all the twenty-seven cubes:

Eight of them represent the whole cube's corners: three of their faces are now red.
Twelve of them, representing the cube's edges, have two red faces.
Six of them, representing the centre of the faces of the whole cube, have one red face.
Finally, you have the centre-most cube, which hasn't been coloured in.

That's a total of fifty-four frosted faces. Since you need to rearrange the cubes to form a large cube that's either solid purple or green, you will at the very least need to colour in that many faces for both of them too. You also need to have them decorated similarly to the layout above, for symmetry's sake if nothing else.

Next, cover three of the faces of the centre-most cube purple and the other half green (but don't frost opposite sides of that cube the same colour). This will let it act as a corner piece for either a purple or green cube.

Then take two of the cubes with three red faces, and colour all remaining faces of one of them purple, the other green. That's two more corners for each coloured cube sorted.

The trick is to leave no wasted space, and to remember only three cubes can be missing one of the colours (i.e. you must have 26 cubes incorporating green, and the same goes for the other two colours). This is permissible since these pieces will double as the centre of the 3x3x3 cube when their missing colour is not being displayed.

Next, let's move on to the six cubes with one red face. Three of them needs to have two green faces and three purple faces, the other three need three green faces and two purple faces.

Why? Because so far we've only covered for two corners each of a green, red or purple cube, and this is how you're going to make the rest. We still need six corners of these three colours total, so we know at least eighteen of these twenty seven total cubes will need to have half their faces painted red, purple or green - six each.

Keeping symmetry in mind, that means the six cubes of three green faces will be divided into three cubes with two red faces, one purple - and three cubes of two purple faces and a red. The same goes for the three red-faced cubes and the three-purple faced cubes, for their corresponding colours.

That leaves only six more edge cubes in green and purple. And what do you know, that's also the EXACT amount of cubes you still haven't completely coloured in frosting! They each have four blank faces, so give them two green and two purple faces each (make sure same-colour faces are adjacent), and your cake is complete!

THE EASY SOLUTION FOR ABSOLUTE CRETINS:

Combine the cubes into one and frost the outside red. Move the bottom layer to the top, then the front of the cube to the back, then the left side of the cube to the right. You now have a new cube uncoloured on the outside. Frost those sides purple.

De-assemble the cube and then paint all unfrosted sides green.

Hello There, I Want To Play A Game...

"Well," remarked Princess Luna, surveying the damage before her, "we would have words with thee, Discord."

"C'mon, Moonbutt," chuckled Discord, spirit of Chaos. "You know Princess Celestia's birthday deserved no less than an absolute belter. The last three were so STUFFY."

He gave Luna a rather pointed look. "Also, it was Fluttershy who suggested I take care of entertainment for the day. Take it up with her."

"I shall," ground out Luna. "And now the entire southern tower is now completely flooded in custard."

Discord rolled his eyes. "Yes, I know. I was there. I promised no Chaos until the party was over. I'd like to go on record as saying it's not my fault the guests weren't fast enough to escape."

"Is that right?" Luna sighed. "Now then Discord, if you could rid all twenty-five stories of this tower of custard? Several ponies will need those rooms later."

Discord looked over at the stone monument he and the Princess were hovering at the top of. He could just about make out a green pony from what appeared to be the sixth floor jumping out of one of the windows, covered in yellow goop and screaming her lungs out.

Chuckling at the sight, he paused. "Seems a shame to waste all this, really..." Discord turned to Luna. "Say, how about we make a game of it?"

"A game?" Luna protested. "Discord, we need this tower back!"

"And you will," Discord raised his clawed hands up. "if you play."

Luna sighed. Truth be told, without the Elements of Harmony, there was very little they could do to actually stop Discord. True, his friendship with Fluttershy reined him in somewhat, but on the days when he was especially bored, it was hard to tell what he'd do next. He did at least promise to keep the Chaos to things that could be easily fixed.

"C'mon," pleaded Discord. "You slept through the party. Didn't even get to the party games part. And I had to be on my best behaviour until the end. Let me have this. Let YOU have this."

It took about a minute of silence, before Luna's face pulled a resigned look. "What are the rules?"

"Aw Moonbutt, you're the best!" cheered Discord. He clapped his hands together. "So! Here's how it goes. We've got twenty-five floors of custard to power through. You and I will take turns draining floors of custard, either one at a time, or three or four at a time."

"And how, pray, will I do that?" Luna asked. "Your Chaos is resistant to all my best banishment spells."

"With this." And with that, Discord conjured up a small plastic straw out of thin air with a snap of his fingers, and handed it to Luna. The straw was striped red and white.

Luna looked at the small plastic tool. "I will assume there's more to this. My stomach capacity has limits."

"Oh, it's special," Discord grinned. "Suck on it once, and it'll vacuum up all the custard in a room, and vanish inside the stomach. Hope you like the taste of cola, by the way."

"Cola?"

"Well, yes," Discord said, as though it were the most obvious thing in the world. "It's CHAOS custard. It won't taste like REGULAR custard. That would be dumb."

"Of course not," Luna said dryly. "And we are to take turns draining each storey of custard until it's entirely gone?"

"Basically," he confirmed. "But you win by draining the custard level to EXACTLY zero. No going over, princess. Oh, and you're not allowed to pass. You have to drain at least one storey every turn."

Luna paused. "So if I drain the custard exactly, I win? And what happens, pray, should I lose?"

"Then I'll flood the towers with custard again, and you'll have to start the game all over."

"WHAT!?"

"It's for the best!" Discord protested. "You just need to win once! That's all! Then I swear I and all my custard will be out of your mane!"

Deep down, the Princess of the Night knew she didn't have much of a choice. Refusing to indulge Discord and having to drain all the custard manually would take far too much time and resources. It stunk of a shell game, but she decided to bank on Discord's restraint regardless.

"Win just once?"

"Win just once."

Luna grimaced. "Restore everything inside to pre-custard condition afterwards, and I'll accept."

"Oh, I knew you'd say that," Discord smiled. "Tell you what. For being such a good sport, I'll let you go first. Take it away, Moonbutt."

Author's Note

Inspired by the fanfics by the infinitely more talented GhostOfHeraclitus. Do check those out.

A tower 25 storeys high is flooded with custard.
Princess Luna and Discord take turns lowering the level of custard by 1, 3 or 4 storeys.
Whoever lowers the level of custard to exactly 0 wins (so no going over 0).
Turns cannot be skipped.
Discord will always play in a way that maximises his chances of winning (in a rare case of deviating from his M.O).
Princess Luna goes first.

PUZZLE: How can Luna win the game and rid the tower of custard?

The Answer 14

The trick is to work backwards from your winning move to calculate a strategy. Ideally, you want Discord to end his last turn on either floor 4, 3 or 1, so you can drain that many floors and win.

Thinking further, 2 is quickly identified as a 'dead floor': you've lost if Discord drains it to that level, since draining 1 floor is your only legal move, and he can drain the remaining floor to win. Floor 7 is the next dead floor, since no move will take Discord down to 2, the next dead level below. The 'dead floors', in other words, floors where you've lost if Discord manages to lower the level down to them, for this tower are floors 2, 7, 9, 14, 16, 21 and 23.

Noticing a pattern? Every dead floor is either a multiple of 7, or 2 greater than a multiple of 7. The rest of the floors are A-OK: as long as you can land on any of those floors, you can win.

All Luna needs to do is drain levels strategically to ensure Discord doesn't send you to a dead floor: if it happens even once, that's it. GG. All he needs to do is keep sending you to dead floors to win. You avoid this by making sure Discord is put on nothing BUT dead floors himself.

Since 23 and 21 are dead floors, Luna HAS to open the game by draining 4 floors of custard to put Discord on the dead floor 21. But from there, it doesn't matter what Discord does, as long as you drain custard to send him to a losing level.

Whew!

The Answer 15

Of course you shouldn't.

it sounds like a 90% success rate from the detector is reliable enough for all purposes, but you forget: the odds of a false reading (10%) is higher than you finding a rock that genuinely has inexplicablyvalumium (1%).

Imagine you searched 1000 rocks. A 1% pull-rate of inexplicablyvalumium means only 10 rocks are expected to have it. As for the other 990, with the detector giving off a false reading 10% of the time, 99 of them can be expected to set it off. That's a total of 109 rocks, and the one in Maud's cart at the moment could be any one of them.

With the odds of that rock having inexplicablyvalumium being 10/109, the odds are seriously stacked against you. There's no real sense in wasting 20,000 bits on what most of the time will be a worthless lump of rock.

Still, the fact Maud tried to pull a fast one on you...she must be a more shrewd businesspony than anypony realised.

"Heh. Didn't think I'd catch you with that. I see why Pinkie thinks so highly of you now."

The Friendship Games Has Too Much Money

The Friendship Games has come around again, and Twilight Sparkle has been asked to help organise the upcoming Hoofball Tournament, pitting all manner of creatures with hooves against one another for international glory.

This year, however, owing to a frankly irresponsible error on the part of the Canterlot Tax Office, the Games has an incredibly large budget for the year and Twilight discovers, to her astonishment, that they are allowing even amateur teams to compete this year, partially to promote the unity theme going on, and partially because all that money needs to go somewhere. Even the Cutie Mark Crusaders managed to pull together a team with the intent of competing against grown adults for the cup.

By allowing just anypony and everypony to compete if they can get a team together, Twilight discovers that there are exactly 12,187 teams competing in the tournament this year. After the poor alicorn princess has managed to come around from fainting (by Spike waving a first edition copy of Jeremy Brenthoof's works under her muzzle), she now has to get started organising the matches.

The tournament is a simple knockout style competition, and with so many teams taking part, there's bound to be quite a lot of matches to play and little time to do it.

So, how many matches need to be played (byes do not counts as matches)?

Author's Note

12,187 teams in the hoofball tournament.
The competition is a simple knockout tournament.

PUZZLE: How many matches need to be played in total?

The Answer 16

Twilight needs to organise 12,186 matches.

In a tournament like this one, when one team loses they are out, so to produce one winner you'd need 12,186 matches to produce 12,186 losers.

Nice Ponies Finish Last

Rainbow stamped at the ground impatiently. She wasn't entirely sure why she, of all ponies, was chosen for an important Royal task that involved having to sit still and be quiet for hours on end.

She had been tasked with meeting with an ambassador from the faraway city of Colarodeo, and was to escort him back home to the airport without causing too much of a fuss. Afterwards, she was to report back to Twilight, with a report of how everything went. It sounded so simple that nothing could go wrong.

The blue pegasus waited for several minutes for him to appear. Eventually, Rainbow decided to just get up and try to find the guy himself. She was warned that he was rather elderly and would need assistance, so she scanned the crowd, hoping to pick him out. It was so much easier when you can fly and get a bird's eye view of everything, all things considered.

Suddenly, Rainbow spotted a grey pony who looked like the photograph, and she hovered over to greet him. Upon meeting him face-to-face, Rainbow noted that he really looked a whole lot older than the photograph, and had a glazed-far-away look in his eye. He was wearing a small golden badge upon a red scarf tied around his neck. Recognising it as the ambassador's mark, Rainbow knew this was the pony.

She decided to play polite and talk to him. "Well...hi? I'm Rainbow Dash..."

"Ah, good morning!" the grey pony replied, in an EXTREMELY wizened old voice. "How do you do do you do do you do...I'm the ambassado-...do you do...how do you do?...I'm the ambassador of...um...do you?...the ambassador of Colarodeo...deo...deo...deo do...do you do? I'm the ambassador of Colarode...do? Er...um, what...what was I trying to say?"

"You're trying to say, 'I'm the ambassador of Colarodeo'," Rainbow ground out, already deciding she wasn't about to get along with him. He was clearly getting on in age, and she had no patience for slowpokes.

The elderly pony stared at Rainbow in what unfortunately seemed like genuine amazement. "So am I!"

"What? No, I meant-" Rainbow smacked a hoof to her forehead. "Ugh, forget it. You're Old Oak, right?"

"...Yes," the ambassador replied, after a wait that took Rainbow too unfortunately long for her tastes.

"Okay! Great! You're coming with me, to the airship," Rainbow said with a hot impatience. The sooner she dropped of the senile old bag of bones, she figured, the sooner she could get back home. She found herself resenting the behavioural standards for ponies with titles. "Hold my hoof, you'd probably just get lost or something...stupid old geezer," she muttered under her breath.

"Rainbow Dash? Is that you?" a classy voice said from behind Rainbow. rainbow turned around, and saw one of Ponyville's resident elegant musician, Octavia. The grey earth pony was carrying a small red suitcase on her back.

"Oh hey Octavia," sighed Rainbow Dash. "How's things shakin'?"

"Things are 'shaking' quite well, thank you," Octavia said. "And who is the gentlecolt with you?"

"Oh hello!" Old Oak seemed pleased to see a new face. "How do you do do you do...I'm the ambassado...do you? How do-"

"Oh sweet Celestia we're NOT doing this again. Sorry Octy, gotta fly, see ya!" And with that, Rainbow Dash dragged the rambling old pony away, towards the airship, much to Octavia's confusion.

Unfortunately for Rainbow, it seemed as though she was going to have to put up with her unwanted baggage for considerably longer than she would have liked. There she was with old Oak, staring at the queue going into the airship to Colarodeo, which she could see was several hundred ponies long at least.

"Aw, jeez!" Rainbow threw her hooves up in resignation. "The line's enormous! What are we gonna do?"

"Oh, don't ask me, you're the ambassador of Colarodeo," said Old Oak, staring at Rainbow, as if expecting her to use her nonexistent authority in some way.

"No, YOU ARE! Gaaaah!" Rainbow groaned, turning her attention to the line again. "Ugh, we're going to be here all day at this rate. Can't you just show your badge or something so we can-"

But in her frustration, Rainbow had forgotten that throwing both hooves in the air meant letting go of the ambassador, and by the time she turned around, she saw he was no longer anywhere to be found.

Panicking, Rainbow took to the air, and within seconds, she saw that Old Oak was somehow right at the front of the queue, showing his credentials to a green earth pony, whom Rainbow guessed was the flight attendant. Breathing a sigh of relief, she flew straight to where he was, just as he was disappearing inside the airship. However, as she tried to get in herself, the attendant whipped out a stop-sign from under her desk, and Rainbow quickly stopped herself mid-air.

"No queue jumping, miss," she said sternly.

"No no, you don't get it," Rainbow tried to explain, landing herself onto the walkway. "He's with me. I'm escorting him home and-"

"Got a pass for that?"

Rainbow paused. Nopony had given her any passes or papers to prove she was supposed to be with him: she was just instructed to meet with him and then don't lose him. "Crud."

"Thought so. Back of the line like everyone else, please."

Grumbling under her breath, Rainbow walked all the way back onto the docking point. She angrily purchased a ticket from the pony at the end of the queue, and impatiently took her place.

She hoped that Old Oak at least remembered his seat number. It was written down on his ticket, so there's no way he could possibly forget...

Unfortunately, everything that could go wrong for somepony like Rainbow Dash very often does, and Old Oak soon found himself surveying the five-hundred empty seats in front of him, asking himself which one he preferred...

Author's Note

I hope nopony ever has this happen to them. Unless you're one of those people who decides to sit in a restaurant 5 minutes before it closes. A special place in Tartarus awaits you if so.

500 seats in an airship.
500 passengers in a queue, with Old Oak at the front and Rainbow Dash at the very back.
Forgetting the number of his seat, Old Oak sits in a random seat.
All other passengers in front of Rainbow Dash sit in their seat if it's available, otherwise they will sit in a random open seat. (Old Oak is too stubborn to move if asked)

PUZZLE: What are the chances of Rainbow Dash sitting in her assigned seat?

A Game That's HARDER The Smarter You Are

Applejack was greeted by a rather peculiar sight. There was Fluttershy, who was shaking a small plastic cup in her hoof, which was creating some sort of rattling sound inside. Next to her was a rather handsome swan, who appeared to be fascinated by the devices in Fluttershy's hooves.

The farmpony had only swung round to Fluttershy's cottage to deliver a large carton of cow guano to help Fluttershy with her own small-scale farm to feed her animal critters, and she was just about to leave the package at her doorstep when she spotted Fluttershy right outside the door, rattling this small plastic drinking apparatus.

Finally, Fluttershy tipped the cup and five small brown cubes Applejack could see were six-sided die tumbled from the cup, finally landing onto the stone floor.

"Eight," Fluttershy said simply, after inspecting the die for about three seconds. The swan then waddled over to the die, and stared at them in polite puzzlement.

"Uh, Fluttershy? What y'all doin'?"

"Oh, hello, Applejack!" Fluttershy looked up from the floor, and upon seeing Applejack, her face broke into a smile. "I'm playing a game with Swansong. I was playing it with Angel earlier, but he kept losing and...um, well, he threw the dice to the floor in a huff and hopped away."

"Not that easy to win, huh?" Applejack chuckled.

"Oh, only if you're unlucky," Fluttershy gave a small smile. "Honestly, it was his idea to begin with, so he's got no right to be upset. I'll have to have a talk with him later."

"Mind if Ah try?" Applejack set the bag down and trotted over to the cup and die lying in a pile.

"Oh, I wouldn't want to encourage GAMBLING," Fluttershy shook her head. "So I've mostly been trying to make this into a different game. A game where you win by figuring out its rules."

She turned to the waterfowl, who was continuing to nudge the die with her beak. "Swansong here hasn't figured out how it works yet."

"HONK?"

"No, it's it doesn't follow those rules, but good try," Fluttershy said encouragingly. The swan looked somewhat despondent.

Applejack's face twisted into a rather confused look, partially because of how Fluttershy could have interpreted Swansong's intentions exactly with a single honk, but also at the premise of the game itself. "Ah'm sorry? You win by figurin' out how to play?"

"More or less." Fluttershy loaded the die back into the cup, and covering the top with her hoof, she started shaking it. "I roll five die, and then depending on how they're rolled, I announce a number. All you need to do, Applejack, is figure out how I announce them."

As soon as she said that, she spilled the rattling die onto the floor, and they fell into a 2, a 6, then 2, then 1, and finally 4.

"Zero."

"That's zero?" Applejack stared in amazement.

"Yes. Angel kept getting rolls like this when he was playing against me. That's why he got so upset."

Fluttershy put the die back into the cup, shook it again, and spilled the die on the floor once again. This time, she rolled 4, 3, 2, 1, and 3.

"Four."

"Wow, this game doesn't sound like it makes a lick o' sense." Applejack shook her head. "What was Angel playin' it with you for anyway?"

"Oh, I told him he couldn't have any more cherries on his dessert, but he wouldn't take it lying down, so he challenged me to this game of die." A regretful look crossed Fluttershy face. "Well, I rolled higher, so it's only fair. He'll just have to live with it."

She loaded the die back into the cup, rolled again, and this time, the die resulted in 3, 5, 6, 5, and 5.

"Fourteen." She looked up at Applejack. "Now at this point, I let you roll, and you need to figure out the result of your roll based on how I did it."

"What?" The farm-pony looked somewhat bewildered. "Sorry Flutters, but it just sounded like y'all just said whatever number popped into your head."

"Oh, no. I said before I follow a set of rules," Fluttershy placed the cubes into the cup, and pushed them towards Applejack. "Go on...um, if that's alright with you..."

Skeptical, Applejack shook the cup as Fluttershy had done three times before, and watched as the die landed on the floor, resulting in 6, 5, 3, 2, and 2.

"So, based on my last three rolls, what's the result of this one?" Fluttershy asked expectantly. She then gave a soft laugh. "Oh my, puzzles really are quite fun. Pinkie was right."

Author's Note

A game is played in which five standard six-sided die are rolled.
All Fluttershy will tell you after the five die are rolled is the answer.
The die rolls, and the assigned answers are as follows:

2, 6, 2, 1, 4. The answer is zero.
4, 3, 2, 1, 3. The answer is four.
3, 5, 6, 5, 5. The answer is fourteen.

PUZZLE: What's the answer when you roll 6, 5, 3, 2, 2?

The Answer 18

The answer is six.

Fluttershy arrives at each answer by:

Noting the die rolls with a dot in the centre (1, 3 or 5 in other words).
Counting all the surrounding dots on those die.

In this case, we have a 5 and a 3. In total they have six dots surrounding them, hence the answer is six.

By the way, if you're wondering why I called the chapter that, it's because this is actually kind of easy, but only if you don't over-complicate things and try to draw upon other elements in puzzle solving you know about to solve this one.

Surprise WITHIN A Surprise? Surprise-ption

Although Princess Twilight Sparkle is no longer Princess Celestia's student, but a fully-fledged Princess with her own responsibilities, Celestia does admit to herself that Twilight does on occasion need to be kept on her hooves to avoid complacency. A prankster at heart, Celestia decides to pull the mother of all pranks on Twilight.

She sends a letter through Spike straight to Twilight, announcing that she'll be visiting Ponyville just to oversee how the School of Friendship and how Ponyville in general is getting on, and just to mess around with Twilight's neurosis and fear of tardiness still further, she won't announce exactly when she'll appear, nor will there be any sign: she won't even use the Royal Chariot for official visits, she'll just teleport straight to Twilight's Castle. All she says in the letter is that it'll be on a weekday the following week after receiving the letter.

After Twilight has gone through enough breathing exercises and paper bags, Spike reminds her that Celestia's probably pulling her hoof, if her pet phoenix Philomena is anything to go by, and the phrase 'pets take after their owners' is any indication.

Twilight then calms down, and decides to think about it logically. Using recursive reasoning, she deduces that Celestia won't be visiting her on a Friday, because after Thursday has passed, if there is no sign of her, she can expect Celestia to visit on Friday, thus ruining the surprise. She then reasons that by the same token, Thursday is out as well, because she'd know by Wednesday if this is the case, and can expect her that day too. She then deduces, going backwards, that there IS no day Princess Celestia can visit her without it ruining the surprise, and she pens a letter back explaining this. She then sets out to perform her duties as head-teacher of the School of Friendship.

Sadly, she's forced to swallow her words (and her ink bottle) when she turns around to the kitchen to eat breakfast the following Thursday morning, only to find the white alicorn munching down on a bowl of bran flakes. HER bran flakes.

Celestia, to her credit, is very patient, and after listening to Twilight fire off several complaints about how she totally went back on her word and all logic (and for finishing off an unopened box of bran flakes in one sitting, seriously, too much fibre can't be good for a pony), she calmly explains that she never lied in the letter she sent once. It was because of a flaw in Twilight's reasoning that led to her total surprise, just as she said.

She then sits Twilight down and asks her to work out what that was, before they set out for the inspection. What was it?

Author's Note

Finally, no number crunching!

Princess Celestia informs Twilight she will make a visit on a weekday the following week, and it will be a complete and utter surprise.
Using recursive logic, Twilight concludes that there's no way Princess Celestia will ever visit that week.
Being Trollestia, she shows up on Thursday (naturally, to Twilight's complete surprise).

PUZZLE: What was the flaw in Twilight's logic?

Music Is Subjective, But Come On

Oof!

Oh my goodness, are you alright? I'm terribly sorry, I wasn't watching myself and...

...I see. I'm glad you're not too badly hurt. ...oh goodness! Your pecan muffins! They're all over the ground! My word, how much are they? I'll pay for another box, it's the least I can do!

No no, I won't hear another word!

Um...I'm sorry for shouting. I'm...told I need to be firmer, but I don't always like it. But I do know sometimes you have to be.

...wait. I recognise you. Are you that pony who helped Pinkie out? She said you always pick up pecan muffins from her place and...

You are? Um...I'm Fluttershy, by the way. If you're that pony, then...could you maybe...solvealittletteenytinyproblemfor me? Um...if that's alright with you...

Oh, not for free, obviously. I'll pay for a new box of muffins. And...maybe a few front row seats to the Summer Sun Celebrations? It's not far off, after all.

I'm in charge of music again, and I've got my usual choir of songbirds ready to play. This year though, I'm not composing the song...um, not entirely. One of the nobles from Canterlot is visiting, and there's a good chance she's coming to Ponyville for it. The song's for her, but she make some rather odd requests for the song.

Firstly, my bird choir is only allowed to sing in four notes: A, B, C and D, all in their major keys. No minor keys here. I can conduct the choir's singing in any order of four sequentially, there are many different combinations, but she said each combination of four must have one note each.

Secondly, I must include EVERY possible combination once and only once.

Thirdly, I am not allowed to change the position of any more than two notes in between combinations.

Fourthly, I cannot have the same note starting or ending each combination any more than twice in a row.

Finally, she wants the choir to be able to sing the song on a loop continuously, without breaking the previously mentioned rules.

Well, I believe once the melody has been sorted out, the accompaniment should be easy to sort out, but if you could compose the main theme for me, I would greatly appreciate it...um...but you don't have to if you don't want to...I'm just saying...

...you'll do it? Oh thank goodness. It's a good thing you like puzzles so much...or that's what Pinkie says, anyway...

Author's Note

I actually had to buy another puzzle book just so I wouldn't have to fall back on the old-hat ones. Here is one of them.

Four birdsong notes A, B, C and D.
You must compose a song featuring every possible combination of notes once each, sequentially.
You cannot change the position of more than two notes in the next sequence.
No same note may be played first or last in more than two successive sequences.
The song must be looped, breaking none of the above rules.

PUZZLE: What should the birds sound like on paper?

The Answer 20

There's several answers to this puzzle, actually. Here is just one of them for your perusal:

ABCD, BADC, BDAC, DBCA, DCBA, CDAB, CADB, ACBD, CABD, ACDB, ADCB, DABC, DBAC, BDCA, BCDA, CBAD, BCAD, CBDA, CDBA, DCAB, DACB, ADBC, ABDC, BACD

Golden_Scroll submitted an alternate solution:

ABCD, ABDC, BADC, BACD, CABD, CADB, DACB, DABC, ADBC, ADCB, BDCA, BDAC, CDAB, CDBA, DCBA, DCAB, ACDB, ACBD, BCAD, BCDA, CBDA, CBAD, DBAC, DBCA

Hogwarts Doesn't Offer Maths

"Maths?" Silverstream repeated. The young hippogriff stared at the professor of the day, Rarity, in confusion.

"Oh goodness, yes," Rarity nodded. "Twilight felt that the School of Friendship should at least include basic education in the curriculum. Celestia knows where I'd be without it."

Gallius let out a groan and threw his clawed font legs in the air. "Urgh, maths is so boring though!"

Sandbar gave the griffon a stern look. "Doesn't change the fact we all need to learn how to count properly."

"Thank you, Sandbar," Rarity smiled at the young colt. She then turned to the blackboard behind her, picked up a white piece of chalk from the pot to the right, and wrote out a series of numbers: 1 to 10, in ascending order.

Gallius stared incredulously at the board, then at Rarity. "Uh, we already know how to count to ten. We're not THAT bad."

Rarity, with her back still facing the class as she continued to write, gave a huge grin. "Oh not that, dear, I assure you." She then went on to chalk down '= 100' next to the sequence of numbers. A collective "Huh?" rang throughout the classroom.

The white unicorn turned back to the class. "I've written down, as you can see, an incorrect sum. What I want is for the class to write down a correct answer to it, using the standard operators."

"Yona not know operators," Yona said, raising her hoof.

"She means symbols such as an addition sign, the subtraction sign, and so on," Cozy Glow explained.

"Precisely. Now observe." Rarity then started to fill in the blank spaces between the numbers, until finally she had written '1 + 2 + 3 + 4 + 5 + 6 + 7 + (8x9) = 100. "This is one such way I could correct the sum. As you can see, I've used nine operators: seven plusses, one multiply sign, and one pair of brackets."

"But there are others," Cozy deduced, seeming to have cottoned on to Rarity's proposed challenge. "There's a certain one you want us to find, right?"

"Oh, my, such a smart filly!" Rarity smiled at Cozy. "Yes, using the standard operators I mentioned, along with the minus symbol and the division symbol, I want the class to find the lowest number of operators needed to make this a correct sum."

"Can we move any of the numbers?" Ocellus asked.

"Not at all. You may, however, combine numbers together to form a larger number. So for example you can treat 3 and 4 as 34."

"Really? All this as part of a maths lesson?" Smolder the dragon asked.

"Well, it's to gauge your current level mostly, so Twilight can better the curriculum," Rarity explained. She looked over the class, none of whom seemed eager to give it a try...except for Ocellus, who was scribbling down possible combinations as soon as Smolder started talking. "Twilight also mentioned a prize for all those who get the correct answer."

Upon hearing those words, Smolder gasped and started scribbling away on her piece of paper. Soon, the rest of the class joined in, with Gallius complaining about how this was designed to punish stupid students, but he picked up his quill and started scrawling away...

Author's Note

Seriously, there should be basic life skills for every school, man.

A sum written as '1 2 3 4 5 6 7 8 9 =100'.
You can use any number of standard operators: +, -, x, ÷ and ().
You cannot move any number's position, but you can combine two adjacent numbers to form one larger number.

PUZZLE: What is the fewest number of operators needed to make this a correct sum?

The Answer 21

You can do it with as few as three operatives.

Don't see how?

Well, if you're still reading:

123 - 45 - 67 + 89 = 100.

Brilliantly simple.

The Answer 22

To reach out to the answer the bucket you must tip,
Enough so that the potion just touches the bucket's lip.

If you can see the bottom, then it's emptier than it seemed,
If the side's partially covered, it's fuller than you dreamed.

But should potion meet the bucket exactly at the joint,
Then it's precisely half-full. I suppose that was my point.

You Probably Would Have Preferred To Play Consequences, Really

It all started at your birthday party that Pinkie had offered to throw for you by way of thanks, both for being such a loyal customer at Sugarcube Corner, partially because your brilliant logic (or perhaps your genre savvy-ness when it comes to puzzles) needed celebrating for whatever unfathomable reason, but mostly because it's your birthday and parties are awesome.

Pinkie offered to have a game of puzzle solving, just for you.

It is rather embarrassing, all things considered. Truth be told, Pinkie's parties are great social get-togethers, but they seem to maintain the consistently filly-ish tone to them. Not to mention you don't even like puzzles THAT much (or maybe you do, given you're still reading this despite the fact it won't exactly go down in history as the Past Sins of your generation).

But since you're here and have for the most part stuck it out, despite how age inappropriate that all the conundrums you've solved for Pinkie and her friends are for a party, heck, even a show's setting like this one, you figure you may as well indulge her this one time as well.

You agree, and Pinkie rubs her hooves in glee before dashing off. She returns pi seconds later exactly (don't try to think about HOW exact) with a series of black and white hats, in as many different styles as your memory can recall the names of: bowler, top, woolly, and so many more, including what looks like Applejack's old Stetson painted white.

You hope that Applejack won't blow up at Pinkie too much afterwards.

Pinkie goes around, placing blindfolds over everypony including you. Judging by the lack of protesting, you figure that this is a puzzle everypony agreed to get involved in. She then places the hats on everypony's heads, fast as lightning, before ending with you.

A sense of familiarity rises within you: there are about six different puzzles you can think of that involve starting this way, but you can probably safely eliminate at least one, given you don't hear the sounds of Pinkie burrowing into the ground, nor the feel of soft earth around your shoulders.

She then guides you to sit in a circle with the other guests before explaining the rules:

Each guest has been given a hat, that is either white or black. There is also at least one of each coloured hat among all the guests. Once the blindfolds are off, you can see each other's hats, but you must not talk or communicate in any way about your hat colour. The challenge put to all guests is to correctly identify the colour of the hat they're wearing. Only one pony needs to guess correctly for the whole group to win. If nopony can answer, or somepony guesses incorrectly, then nopony gets any of that sweet sweet birthday cake that was being saved for the end of the party.

You have to admit that's a gutsy move on Pinkie's part, assuming she isn't bluffing. She hates short-changing guests and leaving them upset, as the ex-holder of the Element of Laughter, so she must really have faith in your puzzle solving skills.

She allows you to devise a plan before removing the blindfolds, but once the game starts, no talking, except for announcing your hat colour.

Frankly, cake is the only real reason to even go to a party, aside from perhaps the punch in large enough quantities, so there is quite the personal stake to succeed here. So how can you ensure that you can determine your hat colour and taste that sweet, sweet baked confectionary?

Author's Note

It's true. There are so many versions of it. But this is the one I'm picking.

A group of ponies each wearing a hat.
The hats are either black or white.
There is at least one hat of each colour.
When the game starts, you cannot discuss the colour of your hat in any way.
If somepony can stand up and correctly announce the colour of their hat, all ponies win the game.
If even one pony does not deduce the colour of their hat correctly, then everypony gets denied your delicious birthday cake.

PUZZLE: What strategy should you suggest everypony follow to earn that cake?

The Answer 23

"Stand up one minute after the number of black hats you can see. So if, for example, you see seven black hats, stand up after eight minutes and announce your hat is black."

Why does this work? Let's simplify it (it's a recurring thing here).

If there were only two of you, and you know there must be at least one black hat and one white hat, you know you're wearing the exact opposite colour of the other pony and both of you will announce your hat correctly.

In the event of three ponies, there would be one of one hat's colour and two of the other. Let's imagine there's two black hats and one white. Anypony wearing a black hat will see one black and one white hat.

If you are wearing a white hat and you can see a black and white hat, the pony wearing the black hat will only see white hats and deduce she's wearing black. But if she only sees one black and one white hat, she won't stand up, not right away. This NON-action allows you to deduce that she can't work out what colour her hat is because she can see two colours and so you conclude you must be wearing black. This goes both ways. If neither of the other ponies stand up, after a while, they'll stand up at the same time.

You therefore need to introduce time intervals for a successful strategy related to hat identifying and use silence as a sort of signalling system, hence this strategy. If you can't see any black hats, stand up after one minute. If you see one, and the pony wearing it doesn't get up after one minute, stand up after two minutes, and so on.

It's a great strategy because there's pretty much no way for you to blow the entire thing by guessing wrong. If you're worried that if you see, say, twelve black hats and stand up after thirteen minutes thinking you're also wearing black, but it turns out white, don't worry.

In that case, whoever's wearing black hats would only see eleven black hats and stand up after TWELVE minutes. There wouldn't ever be a thirteenth minute for you to guess at!

Don't Think It Counts As Fine Print If The Print's All The Same Size

"Announcing Pedant Tick and Duchess Pocket Posey of Canterlot!"

Princess Celestia was shaken out of her idle daydream by the Royal Guard's announcement. After the visit to Ponyville to oversee the School of Friendship (and pull a fast one on her former student - the prankster in her never really left her even in old age), she had returned to Canterlot to take care of all the scheduled Royal Visits. It seemed a slow day was in the cards.

Little did she realise that her foray in logic this morning was set to extend a little further.

The doors out of the throne room swung open, and in stepped a brown stallion with a black mane, dressed in a rather plain but still very formal-looking grey suit and tie, and his companion, a cream mare with a bright azure dress, entered the room.

"Duchess Posey," Princess Celestia acknowledged. "It's good to see you again. Are you and your new foal keeping well?"

"It's new foals, actually," Duchess Posey gave a small smile. "One filly and one colt each."

"Oh my, congratulations!" Princess Celestia gave her most adoring smile. "In that case, are THEY keeping well?"

"Healthy as you can imagine," Posey nodded. "But...it's also led to somewhat of a...complication, if you understand what I mean."

"Complication?"

The stallion who accompanied the Duchess, Pedant Tick stepped forward. "We seem to have reached an impasse regarding the late Duke Ring Rose's will, and we are unsure how to execute it."

"You see," sniffed Posey, wiping a tear from her eye, "as you know, my husband was terribly sick..."

"Ah yes, I do remember," Celestia lowered her head with a tinge of sadness. "It was his one regret, he said. Not being able to live to see himself become a father."

"Of course," Posey fetched a white handkerchief from the pockets of her dress, gave one sharp blow, before neatly folding it away. "Anyway, after he was gone, his will was read out. It said, and I quote, 'In the event that my wife bears a daughter, she is to inherit one third of my entire estate, while my wife is to inherit the remainder. In the event of my wife bearing a son, my wife will inherit one third of my entire estate instead, while my child inherits the remainder.'"

"Ah, I see," A look of understanding crossed Princess Celestia's face. "But you had both a son and a daughter, which complicates matters."

"It seems that he did not include a clause regarding the case of his wife giving birth to more than one foal," Pendant Tick said. "So as you can imagine, we are quite unsure as to what to make of it."

"Well, fear not," Celestia raised a hoof to her chin, deep in thought. "I believe I know of a way to divide the estate fairly while still keeping to the will's stipulations. What you need to do is..."

Author's Note

Judge Judy Princess Celestia. Make it happen.

If a son is born, he will inherit two thirds of the estate while the wife gets a third.
If a daughter is born, she will inherit one third of the estate while the wife gets two thirds.
Twins are born, throwing a wrench in things.

PUZZLE: How can Celestia divide the estate to keep everypony happy?

The Answer 24

Princess Celestia realised Ring Rose's true intention was to have his wife get double the inheritance of a daughter, but half the inheritance of a son.

Therefore, she split the estate into sevenths, sharing it out by giving the daughter one seventh, Pocket Posey getting two sevenths, and the son getting the rest.

Fastest Fillies First (And Second And Third)

"Are you ready for today?"

"Yes ma'am!"

"Sorry, am I talking to a swarm of mice here? I said, are you READY for today!?"

"YES MA'AM!"

"That's what I thought! Now, today's drills! You've got me today to measure exactly how much stamina - or maybe lack of it, frankly, that you think you have! So we're hitting the tracks and you're going to be racing!

"Now as it happens, the other Wonderbolts are using most of the courses on campus, so only one track's been booked for us, but the good news is, there's twenty-five of you and the track's large enough to race five cadets. So at least each race will be fair: five groups of five ponies to race!

"However! I'll personally be watching every race and recording each of your results! And by the end of it, a lot of you will have made it so clear, I said SO CLEAR, how way off you are from being a tried and tested Wonderbolt, that it wouldn't be worth the effort it would take to get you to race again!

"Get it now? Those who actually prove they can outfly a snail in a hurry, I might make you race again just to make sure. So don't you dare think about trying to take it easy just after one win. ANY OF YOU! Anypony who can prove themselves the best three fliers out of all twenty-five of you get lighter duties tomorrow. So I'm expecting a good showing if you care about that at all!

"Got all that, rookies?"

"YES MA'AM!"

"Good to know! Now head to the tracks, in an orderly fashion! We have a long day ahead!"

Author's Note

Ah, what the heck. I did say I had a brilliant puzzle lined up. I'll put it up next. But first:

Twenty-five cadets at the Wonderbolt Academy.
Spitfire wants to identify the three fastest cadets.
Only five cadets are permitted to race at a time.

PUZZLE: What's the minimum number of races needed to find the three fastest cadets?

Slower Is The New Faster

Dangit.

Dangit dangit DANGIT! How'd this even happen? C'mon, Applejack, there's gotta be a diplomatic solution to this horseapples...

...oh, howdy, partner. Ah, don't mind me...

...what's wrong? Ah, it don't concern ya, ya don't need to know. It'd just put ya in a right pickle if ya did.

...ya wanna listen anyway? Well, if ya say so. So, get this.

It all started when Rarity - ya know, who runs the Carousel Boutique - yeah her, she got this customer who was a right pain in the flank to her. Some fancy too-good-for-his-own-horseshoes type all the way from Canterlot. Rainbow Dash got into a right stew about it, and they had a right big argument right there in front of the shop.

Well, one thing led to another and then Rainbow said, "Well, Ah'll bet Rarity could totally beat ya in a race any day!"

...Ah see that look on yer face. Yeah, it went exactly as well as ya think it did.

That guy - Steady Pace, Ah think his name was, he said that she had that bet, and now Rarity's gonna have to run a marathon against that guy for the fate of the Boutique!

She's crazy! No offense to Rares, but magic don't exactly tone yer muscles much, if ya know what Ah mean. Ah guess Rainbow was real sorry afterwards, sayin' she could do it instead, but Rares insists. Somethin' 'bout how she wouldn't want proxies, and that she'd run that race, for the reputation of the Boutique.

Ah mean, not that Ah don't get behind what she's sayin', but she don't stand a chance. Twilight's actually run some simulations on some fancy machine she's got. That Steady Pace did a lot of charity sports events, and he's got stamina to spare, that guy. Much as he was a jerk, that's the honest truth. Now the way he runs, he could do a mile in eight minutes, no stoppin' for breaks or slowin' down. Guess ya don't get a name like that fer nothin'.

Rares, she ain't too bad in short bursts, but she always has to slow down to catch her breath. She reckons she could swap between gallops and trots to save her energy, but her fastest mile was still a second slower than that Steady fella. And Ah'm not one for fancy mathematics, but a second slower is still slower.

So that's it. Rarity's runnin' a race that Ah don't think she could win. Not without cheatin', and where would that leave her even if she won? Ah don't see a way...

...

...yer kiddin'? Ya actually think Rarity could stand a chance? How? Ya don't have some sort of way to pull a fast one on him, do ya? Cos if ya do, Ah ain't advocatin' it.

...ya don't? So's how's Rarity even supposed to beat that guy and keep her business?

Author's Note

I LOVE this one. As soon as I saw it I had to have it.

A 26.2 mile long marathon.
Steady Pace can run at a steady speed of eight minutes per mile.
Rarity alternates between a full sprint and a steady slower jog - the result being she manages a mile in eight minutes and one second.

PUZZLE: How the heck can Rarity win the race?

Cutie Mark Crusader Engineers

Recently, a new sporting event had become somewhat of a tradition in Ponyville: The Applewood Derby. It is a cart race designed to celebrate not only the fastest cart, but also the best looking and most creative cart (Most Creative was wildly considered the hardest category as other competitors always tried to rough up the prettiest one while racing). Eligible for foals of all ages who could drive a bit better than ponies give reasonable credit for, it is quite the draw.

This year, the race had come around again, and the Cutie Mark Crusaders Applebloom, Scootaloo and Sweetie Belle were all putting the finishing touches to the shell of their newest cart. They had switched up the rules this year, turning the race into a team event, where a group of three foals could race in the same cart, and they had all agreed to go for the "fastest cart" prize, since that was by far and away the most simple to achieve.

You didn't need to look pretty to leave everypony else in the dust, after all.

Applebloom screwed the last of the hubs into their place. "There, all done! Well, Crusaders, whad'ya think?"

"Gets the Scootaloo seal of approval!" the orange pegasus filly said, trotting around their cart. "So far. Now, you're sure that you screwed everything in? Last time we built this, you forgot one screw and it fell to pieces after ten yards."

"Yes," grumbled Apple Bloom. "Ah double checked, and then triple checked. Ah'll even do a quad check, just for ya!"

"It's fine," Sweetie Belle raised her hooves in a placating manner. "It'll be fine. Now, why don't we take the cart for a test drive and see how it runs?"

"The good part. Finally," Scootaloo grinned. She hopped straight into the front seat of the cart: not the driver's seat, that was for the leader Applebloom, she knew her role. Sweetie hauled herself into the back seat, adjusting the mirrors slightly with her magic. Applebloom turned the key, and the engine inside the bonnet thundered to life.

The Crusaders emerged from the edges of the Everfree Forest, covered in twigs and leaves, but otherwise grinning from ear to ear.

"Welp," Applebloom declared, "we passed the FIRST test: we didn't crash."

"So far so good," Sweetie Belle nodded. "But how fast were we? Scootaloo?"

"Scootaloo looked down at the stopwatch in her hoof. She raised it to her face, then frowned. "Nowhere NEAR as fast as last year's champ. Two minutes, forty seconds."

"Nuts!" Applebloom kicked the ground with her hoof. "We're 30 seconds shy of Dust Eater."

"Wonder why he was called that if he came first," Sweetie Belle muttered to herself.

"That's not the point!" Scootaloo turned to Sweetie Belle. "The point is that we seriously need to juice up this thing if we wanna start thinking about the fastest cart prize here!"

Applebloom raised a hoof to her chin, in thought. "Well, there's actually a garage on the edge of Ponyville that opened up last year. He came from Manehatten for the quiet life. Ah bet he can give us what we need to soup up the cart!"

"Applebloom, we're FILLIES," Sweetie Belle pointed out. "We're basically living off the pocket money our families give us. And Scootaloo and I blew most of ours on just this cart. I bet he'll be super expensive..."

"Don't y'all worry! I've been savin' all mah bits startin' last year on THIS year. Little by little! Ah reckon a thousand bits should cover the vital stuff."

"A THOUSAND?" Scootaloo's eyes bulged in shock.

"Meh, it's not THAT much," Sweetie Belle had seen more dresses commissioned for her sister Rarity that cost more. "Still a start though. Let's pay the garage a visit!"

"Sure! But, uh..." Applebloom looked sheepish. "It's a mite heavy, so uh...think y'all could help me carry the bag? Seriously, ya'd think SOMEPONY would have invented lighter money. Like paper or somethin'..."

It took a great deal of muscle and a lot of concentration from Sweetie Belle to levitate Applebloom's hoard to the garage, but eventually they found themselves outside a rather oily brown shack. And it was before sundown, so they had beaten curfew, which was a bonus.

"This the place?" Scootaloo asked.

"That's him!" Applebloom grunted, dragging her hard earned dough through the door. "C'mon Crusaders!"

Sweetie Belle and Scootaloo followed in as soon as they managed to step over Applebloom's sack. The three of them found themselves inside a white room, with black oil slicked all over the walls, as though somepony had put oil in a bucket on string and spun it round and round, but not quite fast enough to keep the oil in. They could certainly smell it: they soon found themselves not wanting to stay any longer than necessary. Wooden shelves also littered the walls, with cart engines of various sizes lined up on top, although they also spotted a desk with some basic tune-up kits for sale. Behind that desk was a yellow stallion with probably the most gloriously large grey moustache that were ever seen on a pony.

He looked up from the newspaper he was reading, and spotted his three small customers. "Can I help you with anything?"

"We're entering the Applewood Derby. We need parts. Really good parts." Scootaloo decided to be blunt to speed things along.

"You too, eh?" The stallion chuckled. "Not my first customers today entering the race. Well, most of the fillies came for spare parts, but I've sold most of them off now."

"Not that," Apple Bloom stepped forward. "What have you got in terms of engines?"

"Engines?" He looked rather surprised. "Somepony'd got ambition. And a lot of pocket money." He turned, and motioned towards some of the shelves on the wall to his left. "Well, this is what I've got. Those three engines at the top are by far and away my most powerful - and most pricey. Haven't budged all day though - too much for other fillies' blood, no doubt. Honestly, I thought that Diamond Tiara filly would turn up to buy them, but first come first served, yes?"

"Diamond Tiara?"

"Oh yes. Showed up this morning to inspect my wares. She said she'd come back as soon as she got the bits together. Well, if she made no reservations for my wares, that's on her." He winked at the yellow earth-filly.

Apple Bloom inspected them. They certainly looked impressive. She looked over the specs that were listed to the right of their price tag (400 bits each). According to the owner, and from what Apple Bloom knew about engineering, she could probably shave off about 20 seconds with one of these, but two would make it heavier and reduce the efficiency in half for the second engine...

She then turned to the medium sized engines on the right. She could see eight of them lined up, along with six 5-litre bottles of fuel.

"Ah yes," the stallion explained. "These are my most fuel efficient engines, but that's all down to the special oil they use. Couldn't find anything else for it. Doesn't take regular petrol either, in case you're wondering. But a fully fuelled one has shaved off as much as five seconds from most vehicles. Probably do the same for your cart."

Apple Bloom nodded. "Pretty good."

"Hey," Scootaloo pointed at the cardboard boxes lined up on top of the owner's desk. What are these?"

"Oh these? Tune-up kits." He opened up on of the packets and showed the inside to the orange pegasus. There were all manner of tiny little devices one could install inside an engine to make it more efficient than usual, from fuel consumption to prevention of overheating. "Cheaper than getting an already efficient engine if you know your way around a spanner."

"Geez, we're just spoiled for choice here," Sweetie Belle looked around the garage in amazement, before stopping and putting on a look of deep thought. "So if we buy that, then that, and those..."

"Hold up," Scootaloo trotted up to the white unicorn. "We're the first customers here who wanna buy straight up upgrades. I say we make the most of this opportunity."

"How?" Apple Bloom asked.

"We got a thousand bits to throw at the problem, right?" Both of the other Crusaders nodded. "Then I know what we need to spend it on to make sure we take first place."

Author's Note

Seriously, hurry up and invent notes, Equestria. Or cheques.

NOTE: I'm going on a puzzle hiatus of sorts after this to find more puzzles. I refuse to use the ones that are too well-known to fill a void and so, like the Trick Master from Pokemon, I will depart for a bit.

A cart that can finish a race in 160 seconds.
You have 1000 bits to spend on the cart to improve it.
You can buy:

Three big engines that cost 400 bits each, which shave off 20 seconds each (but if you purchase two, you can shave off another 10 seconds).
Eight medium engines that cost 140 bits each. A fully fuelled one shaves off 5 seconds.
Thirty litres of special fuel for the medium engine: one medium engine consumes 5 litres of fuel for the whole race. 5 litres costs 10 bits.
Four small tune-up kits that cost 50 bits each, which shave off 2.5 seconds each.

PUZZLE: How should the Cutie Mark Crusaders spend their bits to take first place in the race?

The Answer 27

Some of you may have worked out that you should purchase one large engine, three medium engines plus the fuel and three tuneup kits, to spend exactly 1000 bits and shave off 42.5 seconds off the time. Sounds good - if you wanted to get to the finish line the FASTEST for your money.

But that isn't what the question is asking. We want to know how best to spend this money so the CMC can get to the finish line FIRST.

How is that not the same? Think about it. Purchasing the above is possible - but it leaves enough engines, fuel and tune-up kits for an opponent to make the same purchase (or better, if they have enough money for it) and you'll have lost your advantage.

What they actually need to do is purchase two large engines (800 bits and 30 seconds), one medium engine (140 bits and 5 seconds), and all of the fuel available (60 bits). That'll only shave off 35 seconds, but by hogging all the fuel to themselves, the CMC ensure that everypony else can only, at best, purchase a large engine and four tune-up kits to shave off 30 seconds, so they'll win the race by at least 5 seconds.

Rarity wouldn't approve of the sheer greed on display, but what they hay, right?

I Needed A One-Off Character From The Comics For This

Ever since the notorious jewel thief Rough Diamond's humble beginning as a tiny talking horse, she grew into burglary at a frankly alarming rate. She was branded a 'difficult filly', largely because of her penchant for making the school lunches of her fellow classmates suddenly disappear, and no amount of reinforcement, positive or otherwise, managed to dissuade her from stealing the school roof right before graduation.

Her track record had done her no favours when it came to higher education, but far too young and grossly under-qualified and with a sense of guile as big as hers, she was able to use every dirty trick and low-down swindle she could think of to major in Particle Physics and minor in Kleptomania at Manehatten University.

Clutching her new degree in her sweaty hooves, she would go on to mastermind her first bank heist, disguised as Princess Luna (a particularly daring gambit, as Luna hadn't even returned from the moon at the time and nopony recognised her...or perhaps that was exactly why she succeeded), and the theft of Trottingham - as in, the city, yeah, she stole a city - sealing her reputation as one of the most brilliant jewel thieves in all of Equestria.

It is during one such heist that we find Rough Diamond, trying to crack open a safe. As it happens, her plans for the night actually created a schedule overlap with another aspiring jewel thief - she caught him trying to crack it open earlier, but Rough Diamond managed to scare him off by pointing a banana at his head, and he laughed at first, before he would learn to his cost that the banana was in fact loaded.

Turning her attention to the safe. Rough Diamond sees that he's been attempting to open the safe by inserting three different keys into three different locks. Looking over the safe's mechanisms, she sees a large button next to the key locks reading "Attempt to Open". She deduces that once all the keys have unlocked all the locks, the button needs to be pressed in order to gain access to the valuable contents within.

However, the problem soon proves to be trickier than imagined. Rough Diamond has no idea what state the locks are in after the first intruder left, and the locks seem to function independently, so no hope of fiddling with one to hit a reset button for her. What's more, she cannot fiddle with a lock to figure out if it's locked or not, as the lock is one where the key doesn't need to be turned to change its state.

She doesn't have all night. She reckons as long as she goes through the right number of sequences, she should be able to get the safe open eventually, but how long would that take?

Author's Note

Couldn't find a recurring master thief in the main show.

You have a safe with three locks: 1, 2 and 3. Each one is is unlocked by one of three keys: A, B or C.
To open the safe, each of the keys must be inserted into a lock and then somepony must press a button labeled “Attempt To Open.”
The locks function independently.
If the correct key is inserted into a lock when the button is pressed, that lock will change state — going from locked to unlocked or unlocked to locked.
If an incorrect key is inserted in a lock when the attempt button is pressed, nothing happens.
You don't know the statuses of any of the three locks.

PUZZLE: What is the minimum number of attempts that will guarantee that the safe opens?

The Answer 28

You'll need at least thirteen attempts to assuredly open the safe.

We have three keys and three locks, and so we have six different ways we can arrange the keys to assigned locks. Depending on how they're arranged, one of five things can happen:

Nothing happens.
The first lock changes state.
The second lock changes state.
The third lock changes state.
They all change state.

We also have three locks in two possible states: locked or unlocked. We therefore have eight different possibilities when it comes to how the locks could start off as. And because we don't know how each lock was at the start, we have to go through ALL possible combinations to guarantee the safe opens. So we can't do any better than eight tries, but we can make sure we don't do worse than thirteen. Try opening it by inserting each of these keys in the locks ordered 1-3 in this order:

ABC, ABC, BCA, CAB, ABC, BCA, ABC, ACB, BAC, ACB, CBA, BAC, ACB.

S.P.L.A.T (Society of Ponies Leaping from Alpaca Towers)

"Hey," Applejack gestured at Rarity. The white unicorn looked up from her book. "Yes, Applejack?"

"Ya ever wonder why we're here?"

"Are you talking about our current predicament, or is this an attempt to wax philosophy to pass the time?"

"...uh, first one," Applejack looked confused. "Ah mean, Ah don't get what happened. One moment we were just talking real peacefully to the alpaca tribe's leader, and next thing we know we got cuffed and thrown right atop this tower. Was it something we said?"

"I mean honestly, all I suggested was that they build another boat if they wanted all their grain, chickens and wolves across the river faster, but this seems...disproportionate." Rarity shook her head. "My fault, I suppose. I should have realised how ill-mannered and stubborn those brutes could be."

Fluttershy sniffed quietly. Rarity pulled her towards her in a comforting embrace. "It'll be fine, darling. We'll find a way out."

"Oh I know..." Fluttershy shook her head. "I can't help but worry, though."

Applejack trotted over to the tower window, and looked down. "Welp, we sure ain't climbing out. We'd splat on the floor like one of mah Granny's apple fritters."

"And no attempt at lock-pickin on my part or bucking can open this door," added Rarity, struggling with the doorknob as best she could, given the lack of opposable thumbs. She turned to Fluttershy. "Darling, do you think you could fly us out?"

"Um..." Fluttershy looked out of the window, and upon seeing the drop below, she quickly backed away. "EEP!"

She turned to the others. "Sorry...not good with heights. But, not really...my wings still haven't fully recovered from yesterday. If I tried carrying you out, I'd probably drop you..."

"It's alright darling, we're not going to force you," Rarity struggled with the lock for another five seconds before finally throwing the hairpin to the floor. Finally giving up in disgust, she was about to make her way back to one of the chairs in the centre of the room, when several items propped up against the wall caught her eye.

"...Say, I do believe I have an idea..."

"Somethin' to get us out?" Applejack's eyes lit up.

"Of a sorts..." Rarity appeared deep in thought. She motioned to a large stockpile of goods in the corner. "I cannot help but notice a rather long sturdy rope, and two crops baskets."

Using her unicorn magic to levitate the objects towards her, one at a time, she turned to the others. "I believe I may be able to assemble a makeshift pulley system so we can escape via the window."

"Like an elevator?"

"Of sorts," Rarity nodded. "Of course, whether I can design one strong enough for all three of us is..." Rarity scrunched up her face. "This is...VERY uncomfortable for me to ask this, goodness knows a proper lady would never make such an enquiry, but..."

"Rarity, there ain't any polite society to offend here," Applejack pointed out.

Rarity struggled with herself before finally blurting out, "How much do you both weigh?"

A poignant silence filled the air. Rarity flailed her hooves in the air. "It's for the pulley system! I'm not a gossip! ...not MUCH of a gossip anyway."

Fluttershy nervously trotted over to Rarity, before whispering something in her ear. "I see...thank you, that helps."

"Oh...um, you're welcome..." Fluttershy hid her face in her mane out of sheer embarrassment. "...I try to watch my weight..."

"Ah, horseapples," Applejack sighed. "Fine, but this doesn't leave the tower, okay? Not havin' anypony think Ah'm tubby."

"My dear Applejack, there are some lines a lady must NEVER cross!" Rarity insisted. "Rest assured your secret will be safe with me!"

Applejack nodded, and whispered her weight into Rarity's ear.

"Alright...so...I believe we should be able to get out...I would say that as long as we don't go thirty pounds over the weight limit, we should be able to avoid a very messy spill..." Rarity was muttering to herself as she drove a large nail with her magic into the outside walls of the tower. She then tied both ends of the very long rope to each of the crop baskets, before carefully throwing the rope over the nail in a loop, creating her makeshift elevator.

"Are you sure this is...safe?" Fluttershy was beginning to shake.

"Of course!" Rarity said haughtily. "...in theory," she added, sounding less confident.

"In theory?" Fluttershy squeaked.

"Well, we're stuck here until those infernal alpacas destroy themselves with their own stubbornness, so it's the pulleys or bust, darling."

A look of concern crossed Applejack's face. The unstable elevator was already bad enough, but there seemed to be a more pressing concern. "Didn't ya mutter to yerself that we couldn't go over thirty pounds in weight? Ah mean, Ah'm not sayin' Ah'm fat..."

"Naturally!"

"But Ah'm pretty sure Ah'm well over Fluttershy."

"True..." Rarity scanned the room for something she could use to solve such a problem. "I think we could all escape, if I had something that weighed one hundred and fifty pounds. That should balance the weight enough for all three of us..."

"Um...like this big bronze statue?" Fluttershy pointed to what appeared to be a bronze bust of Princess Celestia, that had been rather extensively graffiti'ed all over in a red ink marker with all sorts of offensive slogans.

"Well, I suppose, but I would first need to make sure..."

"It's one hundred and fifty exactly. I checked," Fluttershy said, pointing to the weight, carved into the back of the statue, along with another note that said "Made in China".

Rarity could only stare in amazement. "What an astonishingly contrived coincidence..." She shook her head, and summoned up her unicorn magic again to move the statue to her. It seemed to be a bit of a strain for her, given the strained look on her face and the extra glow to her horn. "Well, no time like the present, you two! Let's hurry up and get out of here before they notice we're plotting an escape!"

"Where the heck's China...?" Applejack wondered out loud.

"Applejack!"

"Alright, keep her mane on, Ah'm comin'..."

Author's Note

Not doing that stupid liquid in jugs one. No, I don't really care that this uses similar logic, shut up.

Rarity, Applejack, Fluttershy and a bronze statue atop a tower.
A pulley system with a rope and two baskets set up outside the tower.
If the contents of a basket is heavier (by over 30 pounds) than the contents of the other basket, the heavier one will fall, dooming the ponies inside to a rather splattery end.
All occupants are of the following weights:

Applejack: 370 pounds.
Rarity: 210 pounds.
Fluttershy: 180 pounds.
Statue: 150 pounds.

PUZZLE: How can you get all three ponies out of the tower safely?

The Answer 29

Send the statue in the basket down to the bottom.
Fluttershy then gets in the other basket and goes down, sending the statue back up.
Rarity removes the statue while climbing inside the basket, sending her down, while Fluttershy goes back up.
The statue is then thrown out of the tower down to the bottom. It's not a living creature, so feel free to be as careless with it as you like.
Rarity and the statue are then loaded in the bottom basket while Applejack gets in the top basket. AJ goes down, Rarity and the statue go back up.
Send the statue in the basket down to the bottom again.
Fluttershy then gets in the other basket and goes down, sending the statue back up.
Rarity removes the statue while climbing inside the basket, sending her down, while Fluttershy goes back up.
Once again, chuck the statue out to the bottom of the tower.
Load the statue in the basket, and let that balance the weight to allow Fluttershy to come back down!

Curses!

It all started, as all good field trips are want to do, with a trip to a field.

Well, more specifically, it had been to a strange underground temple right UNDER the field, on the outskirts of Ponyville.

Rainbow Dash had taken a class from the School of Friendship down to the ruins to explore, partially to help with the whole cooperation and teamwork thing that friendship is all about, but also to indulge her inner Daring Do fan-filly regarding these ancient ruins. And as long as the students didn't catch on to things like how they were only painting the fence or waxing a wagon for a two-for-one deal and not for a friendship lesson - or karate - just about anything went.

It had gone well - right up until the moment a fight between Gallus and Smolder broke out (it had something to do with gingerbread spiders, apparently) just as the group had made their way straight to the heart of the temple, and it was during their ensuing scuffle that they knocked over what looked like a priceless pottery piece, causing it to shatter on the floor.

Rainbow Dash, being such a fan of Daring Do, would have declared this moment the exact point in time where all the booby traps in an ancient ruin would suddenly activate and attempt to end the heroes right then and there, and because nopony would ever want this temple to be accused of not following tradition, the walls start to shake and rumble, and two wisps of a weird purple gas escapes the shattered pot.

Taking the class to safety, Rainbow leads the class right back to the first room they entered upon reaching the ruins, which has five different corridors, including the one they just came through. One of the corridors leads back outside, while the others are dead ends (or at least they wouldn't be if they weren't currently attempting to flee for their lives and there were time to study the murals on the walls).

Rainbow spots an ancient clock at the centre of the room, telling her she's only got an hour left before the temple apparently collapses and future archeologists find their remains and put their decayed forms on coffee mugs and mouse-pads in tourist gift shops. From what she remembers from the trip, she reckons there's just enough time to explore one corridor, return to the room to report and then escape back outside, as long as she splits the class off into groups. There's nine of them, including herself.

Unfortunately, nothing seems to ever be that simple. The corridors are just too narrow for Rainbow to fly at speed, and from the murals' description (helpfully written in the modern tongue, which was useful since Rainbow wasn't an obsessive nerd who messed around with hieroglyphs) the two wisps of smoke were in fact the vengeful spirits of an ancient high priest Tim (of Tep) and his lover, and they would possess travellers and lead them to their doom, involving a disturbingly high amount of scarab beetles.

Rainbow realises that two of the class are possessed, and could lie at any moment, but they may also tell the truth - nopony could ever accuse them of being impractically evil. As they won't lie all the time, Rainbow has no way to tell them apart, except for the fact that she definitely isn't possessed, and that she's the only one in the room aware of the curse.

And so, to avoid a rather grizzly end (and a rather awkward parent-teacher conference afterwards), how should Rainbow Dash play this in order to make sure she and the class get back in one piece?

Author's Note

Nine in a group, including Rainbow Dash.
Four branching paths.
There's only enough time to explore each path once (at the same time), return to the room, and escape down the exit.
Two of the group (excluding Rainbow) could lie about the exit's location at any time.
There is no way to differentiate the two liars from the others.

PUZZLE: How can all of the group escape via the exit?

Another Will To Sort Through

"Announcing Pedant Tick, Fancy Pants, Upper Crust and Duchess Pocket Posey of Canterlot!"

Princess Celestia glanced up at the throne-room doors, and spotted four ponies enter the room. Two, she recognised as Pedant Tick and Pocket Posey, and two newcomers. Searching the back of her mind, she recognised Upper Crust from her days as a rather notorious art sponsor, and the blue stallion known as Fancy Pants, who had attended many charity events within Canterlot with his wife.

Wondering exactly why three seemingly unrelated ponies would request a joint-audience with her, she stepped down from her throne to greet the quartet. As she approached them, Upper Crust saw fit to bow, but Celestia gave a small smile. "Rise, my little pony. There is no need for that here."

Her attention then turned to Pedant Tick. "Ah, hello, Pedant. A pleasure to see you again."

"And the same to you, your highness," nodded Pedant. "I am truly sorry to have to impose upon you again, but..."

"It is no trouble at all," Celestia gently assured him. "I will always find time. Now, what seems to be the problem?"

Fancy Pants stepped forward. "Do you remember the Mr Crystalling, the pony otherwise known as The Collector?"

"Ah, yes," Celestia raised a hoof to her chin in thought. "He was an avid jewel collector, was he not? He had received such fame that he found himself the constant target for thieves, most unfortunately. Fortunately, he was also an expert forger, and he put those talents to use by creating exceptional fakes, to a point where hardly anypony believed he had anything genuinely valuable in his estate anymore."

"The very same," Pedant said, reaching into the pocket of his suit and pulling out a piece of paper. "As it turns out, absolutely everything that was stolen from him were all fakes, and his genuine collection of valuable treasures was discovered shortly after his passing."

"My goodness!"

"Indeed. It turns out he was entirely fond of my three clients here, and he left his entire collection of valuable jewels to them, to be divided equally."

"I'm sensing a 'but' here..." Celestia said slowly.

Pocket Posey chose this moment to speak up. "But the will states we get to choose from his spoils in a certain order, and none of us have any clue who gets priority!"

"And why not?" Celestia asked, in a rather puzzled tone.

"Priority seems to be based on certain events in our lives," grumbled Upper Crust. "As if I could possibly remember where I was fifteen years ago!"

"You see, your highness," Pedant said, passing the will to Celestia for her to read, "none of them remember the relevant facts stated in the will, and we have no way of knowing whether if The Collector remembered the events with any clarity himself. We're choosing to proceed under the assumption he did, however..."

"It is rather shameful of us," Fancy Pants lowered his head in shame. "How could the date I first knew my darling Fleur was the one slipped my mind?"

Celestia scanned the will over several times, before handing it back to Pedant. "I believe I have a solution."

"Truly?" Pocket Posey gasped. "Do you remember when we...?"

"Oh, Pocket," laughed Celestia. "I am over one thousand years old, but I'm afraid my memory isn't quite THAT long." She turned to address the four ponies. "Perhaps if we were to treat this will as a puzzle of sorts, then I think it is possible to INFER the order. You see..."

Author's Note

So can you solve it? it's a bit trickier than the last will, yes?

Three ponies: Fancy Pants, Upper Crust, and Pocket Posey.
A will that reads as follows:

"I leave my jewel collection of 39,000 jewels to be shared equally among Fancy Pants, Upper Crust and Pocket Posey, who are to choose in a certain order:

Nopony who has ever seen me wearing a red hat is to choose before Fancy Pants.
If Upper Crust was not in Canterlot's tallest tower 15 years ago, the first chooser never lent me an umbrella.
In the event Upper Crust or Pocket Posey gets second pick, Pocket Posey comes before the first of the three ponies to fall in love."

Fancy Pants, Upper Crust and Pocket Posey don't remember any of the relevant facts.
All statements are to be treated as non-superfluous.

PUZZLE: In what order do the three ponies get to pick out the jewels?

The Answer 31

The order is Fancy Pants, Pocket Posey, Upper Crust.

It DOES sound like we haven't got any new info to go on, doesn't it? If nopony can remember the exact details, then how can the order be sorted out?

Well, the trick is to, as the puzzle's summary stated, treat the statements as non-superfluous - in other words, each statement MUST provide some useful information about the order. If they can't tell us anything then the solution you're thinking of is wrong. No ifs and no buts.

Let's talk about the first clause. In order for this statement to actually tell us anything, at least Upper Crust or Pocket Posey must have seen The Collector in a red hat, because otherwise the statement would be entirely worthless. Therefore, Fancy Pants can't be the third-chooser, as he must be followed by a pony who saw The Collector in a red hat.

Moving on to statement 2, if Upper Crust was in Canterlot's tallest tower 15 years ago, again, the statement would tell us nothing new, so she couldn't have been there. And if nopony lent The Collector an umbrella then the statement is superfluous. Therefore, somepony MUST have lent him an umbrella. But who?

If Fancy Pants were that pony, then he won't be coming first. We know from the first clue that he isn't last in line, so this would put him second. But if he IS second, that would render the third clue (the one about falling in love) useless, and make the puzzle unsolvable. So Fancy Pants never lent The Collector an umbrella.

Assuming both Upper Crust and Pocket Posey lent The Collector an umbrella, that would mean Fancy Pants would be first in the order, making the first statement superfluous. So one or the other lent an umbrella, but not both. Likewise, if Upper Crust and Pocket Posey both saw The Collector in a red hat, then Fancy Pants would be first, rendering the second clue superfluous. So one or the other saw The Collector in a red hat, but not both.

Now, let's assume the possibility that Upper Crust BOTH lent an umbrella and saw a red hat. From clue 1 we know she can't be first, which would render clue 2 superfluous. So if she did one thing, she cannot have done the other. The same logic applies for Pocket Posey: she must have done only one of those things.

In both cases, Fancy Pants would be first, and so, from the third clue, Upper Crust must have been the one to fall in love first, and so the final order is Fancy Pants, Pocket Posey and Upper Crust.

Those Who Want Money And Those Who Want A Bit More Money

"Bon Bon! BON BON!"

Bon Bon massaged her sore head, nursing a thumping headache over the strongest coffee she could make that morning. She was wearing her pale blue nightgown and was sitting at the breakfast table, enjoying the peace and quiet, until her housemate, Lyra Heartstrings, came jumping down the stairs in giddy excitement, clutching what appeared to be yesterday's paper in her hooves. "I did it, I did it!"

Bon Bon sighed. "I swear to Celestia if your petition to turn all the benches in Ponyville into reclining massage chairs got passed by City Hall..."

"Not that!" Lyra shoved the paper straight into her friend's annoyed face. "Did you read that article yesterday? About that eccentric billionaire?"

"Hmm? Oh, that guy? That guy who said he'd give his fortune to the first pony to submit the correct answer to a puzzle he had held on to since birth?"

"That's him, that's him!" Lyra nodded quickly, her grin never leaving her face. "Well, GUESS what happened?"

"...I dread to ask, but you solved it?"

"I SOLVED IT!" Lyra shouted excitedly. "All by myself! Fame and fortune call to me! The riches are mine for the claiming!"

"Lyra, be reasonable," protested Bon Bon. "As far as I remember, it was just a three-colour map puzzle: one of those ones where you have to colour in parts where no two matching colours touch. It was hardly the most mind-blowing riddle of the ages here. Somepony's probably already submitted the answer and is enjoying their new riches right about now."

"I think not!" Lyra protested back. "he said you have to turn up to his residence with the answer before you get the money, and it's so far out that NOPONY could ever get there on their own!"

"Including you," Bon Bon pointed out.

"Nuh-uh! I'm heading to the bank to borrow the cash for the trip. By the time I'm back we'll be rolling in it! Wish me luck!"

"Wait, aren't you going to have breakfast..." Bon Bon began to say, before Lyra zoomed out of the house and slammed the door on the way out. "...first?"

She looked down at her coffee. "This isn't strong enough for the morning anymore. I just know it."

"Miss Heartstrings, I can't just loan 10,000 bits to you without you explaining WHY," Tender Lender, Ponyville's bank manager, sighed in frustration. It had been a difficult start to the morning. First, minutes before she was about to open the bank, she spotted a green unicorn hammering away at the doors of the building, demanding entrance and swift vengeance to all who would deny her, before she was made to sit and wait for 8 am like a civilised pony. As soon as the clock struck eight, she promptly galloped inside and demanded a loan of 10,000 bits to Tender Lender's face.

"I told you, it's so I can make a trip to an eccentric billionaire's secret hideout so I can claim my reward of 10 million bits for solving a puzzle in the morning newspaper!" Lyra threw up her hooves in frustration.

"Well..." Tender Lender pushed her glasses up, trying to regain her composure. "My congratulations, i suppose." She pointed to the piece of paper Lyra was clutching in her hoof. "Forgive me, but is that the puzzle there?"

"Yes. And no, you can't look at it."

"Miss, I am not prepared to give out a loan you may not be able to pay back. You are relying entirely on yourself receiving this 'reward' of yours to pay back the interest." She reached out her hoof. "Can I at least confirm it's solved? So that you don't spend a wasted trip?"

And so Lyra had hit an impasse. Simply showing the solution to Tender Lender wouldn't do: her rampant paranoia made her afraid she would simply kick Lyra out of the bank and take the reward for herself. She briefly toyed with the idea of varying degrees of bodily harm or threats, but decided that the thought of needing to pay for all legal fees plus her distrust of those in the legal profession soon put a stop to that.

In fact, Lyra felt that in order to minimise attention, she needed to keep this between herself and Tender Lender. Nopony else was to know. No media outlets, no lawyers, no middleponies, and especially no turning for help to convince the poor bank manager.

She decided that if there was any time to prove her worth as a puzzle solver worthy of such a fortune, this was surely it.

Author's Note

Looking suspiciously at you, Ri2.

You have a three-colour map puzzle.
You want a loan of 10,000 bits from Tender Lender.
Tender Lender won't give the loan unless you can prove you actually have the solution to the map puzzle.
You do not want to get anypony else involved in your affairs.

PUZZLE: How can you prove you have the solution without giving it away, or giving enough away for Tender Lender to reproduce it?

Why Do So Many Puzzles Involve Being Imprisoned Somewhere?

You're awake! Thank goodness! You were out for ages!

Well, five minutes, but my point still stands. AGES!

That was a pretty bad knock to the head you took. Are you okay? Do you remember who I am?

Yeah, Rainbow Dash. So at least you don't have amnesia or anything...or do you? Do you remember your name?

...

...Alright, I think you're okay.

Gaaaah, stupid alpacas! I thought I could avoid getting captured like Rarity, AJ and Fluttershy did, but those guys are stronger than they look...

...

...doesn't look like they intend to let us out any time soon.

What are you in here for, anyway?

...you on-upped the king on a puzzle and he decided to throw you in jail!? That's stupid! What's wrong with being an egghead? I wouldn't mind being one! Professor Egghead wouldn't just be a name for the School of Friendship anymore!

Me? Oh, well, I got called out by the Map. Yeah, the Cutie Map. Twilight's castle has this map that sends us out anywhere there's a friendship problem. And really, these guys are SERIOUSLY not the most friendly bunch you ever saw, huh?

...is anyone actually coming for us? HEY! HEY! LET US OUTTA HERE, YOU STUPID STINKING BUNCH OF -

Uh, nevermind. That got his attention...

...so. We're doomed. The jailer sets us up to play this weird game, and if we both lose, we're staying here in the dungeon forever.

...Geez, how can you just stay so calm? Look, I know he said that if we win, we go free, but c'mon! There's no way we're ever going to get outta here! You know one of us is going to screw up! One hundred chances at it!

...do you not hear what we're supposed to be doing? Okay, i'll repeat it slowly, so you know how utterly DOOMED we are.

He's going to take us away to separate cells. He'll then make us toss a coin, and then we gotta guess if the other pony got heads or tails. If we both guess correctly, WE LOSE! I mean, I'm a pretty unlucky pony. I get into scrapes flying all the time. There's no way we're ever going to pull through a hundred flips and not get the guesses correct!

...you have a plan?

...Oh you're the best! Not bad, for an egghead! Okay, we'll do that...

Author's Note

Well there are. But I've never heard this one before, so I'm going with that.

You and Rainbow Dash to be separated into different cells.
You will both toss a coin, and must predict if the other got heads or tails.
If both of you guess correctly, you will both be imprisoned FOREVER.
Manage one hundred flips with at least one incorrect guess every time, and you go free.
Once separated, you will not be able to communicate with one another in any way.

PUZZLE: Before being separated, discuss a strategy. How can you both last long enough to go free?

The Answer 33

Use the same outcome of your own coin flip to predict Rainbow Dash's flip. Rainbow Dash should predict your flip based on it being the opposite of HER coin flip.

Sounds too simple to be true, but it works. As long as at least one of you gets a prediction wrong, both of you are still in this thing. Below are all the possible scenarios that prove this strategy works:

If you flip heads and Rainbow Dash flips heads too, you would predict heads and Rainbow would predict tails. That's one incorrect answer and you're still in the game.
If you flip heads and Rainbow flips tails, you would guess heads and Rainbow would guess tails. This time YOU'RE wrong, and you both get to live.
If you flip tails and Rainbow flips heads, you call tails and Rainbow calls tails. Again, an incorrect answer on your part spares you both.
If you both flip tails, you would call tails and Rainbow would incorrectly guess heads.

Team Egghead: 1, Jailor: 0!

It Was Such A Lovely Day, Too

"So," Twilight Sparkle narrowed her eyes at the two ponies she had called into her office, Starlight Glimmer and Trixie. "Would either of you care to explain exactly what happened?"

Starlight and Trixie both turned their heads at each other, before nervously making eye contact with Twilight again. "Uh..." Starlight started, "where's the other one?"

Twilight sighed. "I HAD called them into the office too, but unfortunately they were cunning enough to skip town and lie low for a bit. You two, however, have no such excuses. So I'm asking you, again, exactly what happened."

Starlight started to shuffle nervously from hoof to hoof. Trixie, it seemed, was the only one brave enough to volunteer a response. "A lot happened. Trixie asks that you be more specific."

Twilight rubbed her forehead in frustration: it would seem Trixie's cheek was at least still intact after their ordeal. "Let's start then, with the report I got back from the Camel Kingdom. The two of you had arrived right outside the palace..."

"Uh huh," Starlight nodded.

"...where you met up with our too-smart-for-their-own-good friend, where they were vacationing after the stint in prison with Rainbow Dash last week..."

"Yyyyyup," Starlight said.

"...when a riot suddenly broke out in the town square due to Trixie's incredibly rash actions - "

"That pigeon had it coming!" Trixie suddenly shouted. "Ruined my hat with its droppings!"

"We didn't even know it was the favourite pet of the Camel King, we just got there!" Starlight threw up her hooves in protest. A thoughtful look crossed her face. "Having said that, aiming your entire stock of fireworks onto said pigeon was a bit overkill..."

"...great, so you admit it," Twilight groaned. "I swear the Map's going to call us out again just to apologise and patch up connections. So, WHY, exactly, were all three of you arrested when Trixie was evidently the sole aggressor?"

Starlight was trying very hard not to burst out laughing by gritting her teeth. "She...uh, made us hold the fireworks. We got arrested as accomplices."

"Good friends help one another, and I needed your help!" Trixie explained, as though it were the most obvious truth in the world.

Twilight raised a hoof to forehead again with an audible slap. She then held the report from the Camel Kingdom back up to her face. "You were then arrested for attempted assassination of a royal pet by two armed guards- "

"Three armed guards," Starlight raised her hoof, feeling a rather pedantic need to correct the purple alicorn. She soon found herself regretting that decision, as Twilight's angry face only grew angrier.

"THREE armed guards, then, where you spent a period of six hours before being released." Twilight glared at the pair. "How, exactly, did you three manage to avoid being found guilty and sentenced?"

"Oh, that pony, the puzzle-master, talked the jailor into giving us a chance," Trixie explained. "The jailor likes games and so he decided we bet to stake our freedom on one."

"And you won?"

"Evidently," Trixie said dryly.

"Don't back-sass me!" Twilight hotly shot back at the blue unicorn. She sighed. "So..." Twilight continued on, "what were the terms?"

"Well we weren't alone in the cell," Starlight explained. "There were twenty other prisoners in the jail, all of them also jailed for the same crime, under similar circumstances - "

"What, attempting to shoot the royal pigeon for leaving its...leavings, in the mane and clothes?"

"Really, you'd think it just does this on purpose. Trixie thinks it's doing it on purpose," the blue unicorn declared, adjusting her hat to hide the smirk on her face.

Starlight coughed. " - and we were all in the same boat, so they were playing with us. He explained we would be escorted to this room, one at a time, at random, where there were two switches, which were either on or off. We then had to either change the position of one of the switches, or leave it as is."

"And then?" Twilight raised an eyebrow.

"Well, if one of us could declare that all twenty-three of us had visited the room at least once, we'd all get pardoned and go free. If we got it wrong, we'd get fed to the prison's gingerbread spiders."

"Gingerbread spiders...and I thought that was just a mistake on the part of the written report..." Twilight sounded a little surprised, but it quickly passed, as her voice and face took on an angry mask once again. "And you succeeded?" she asked sharply.

"Basically. It was all the other pony's idea though. We just did as told."

Author's Note

Tune in for Part 2! Unless you don't solve this one and you cause a time paradox, or something.

23 prisoners, including you, Starlight and Trixie, isolated in separate cells.
There's a room with two switches: 1 and 2.
The switches are either off or on, but you can't tell their status just by looking.
Prisoners will be escorted to the room where they can either change one of the switches' position or leave them.
Prisoners to be led to the room are randomly chosen: the same pony could be led to the room more than once, or not chosen at all. They'll then be led back to their cell.
You are freed by having one of the prisoners announce that everypony has visited the switch room.
If they are wrong, they are fed to the gingerbread spiders.

PUZZLE: Before being separated, what strategy should you suggest everypony follow to get out?

The Answer 34

In order to escape, you need to introduce some sort of means of keeping track of prisoners, and that means having to assign outcomes to tasks. The easiest way to do this is to nominate one pony, a 'leader' who will act separately from the other twenty-two prisoners, while the rest take the same actions.

The group agrees upon the following rules:

The leader is the only person who will announce that everypony has visited the switch room. All prisoners (except for the leader) will flip the first switch up during their first visit to the room, and again on the second visit. They are only to flip the second switch if the first switch is already up, or this is their third or more visit to the room. Stress that ONLY the leader may flip the first switch DOWN: if the first switch is already down, then the leader will flip the second switch.

By making sure that the leader is the only one to take the unique action of flipping the second switch down, it becomes a means of tracking how many people have visited the room, by remembering how often the leader has had to move the second switch down. Once the leader has flipped the first switch down forty-four times, they announce that all have visited the room.

It does not matter how many times a prisoner has visited the room, in which order the prisoners were sent or even if the first switch was initially up. Once the leader has flipped the switch down forty-four times then the leader knows everyone has visited the room. If the switch was initially down, then all twenty-two prisoners will flip the switch up twice. If the switch was initially up, then there will be one prisoner who only flips the switch up once and the rest will flip it up twice.

Why forty-four? Because the prisoners can not be certain that all have visited the room after the leader flips the switch down 23 times: it could be that the first twelve prisoners plus the leader were taken to the room twenty-four times before anyone else is allowed into the room. Because the initial state of the switch might be up, the prisoners must flip the first switch up twice. If they decide to flip it up only once, the leader will not know if he should count to twenty-two or twenty-three.

Fssssssssssssssssssssssssssssh

Twilight raised an eyebrow at Starlight and Trixie. "So, after the three of you had earned your freedom, what happened next?"

Starlight and Trixie nervously glanced at one another. "Honestly Twilight," Starlight offered, "there's nothing to tell. The three of us managed to make it back to Ponyville after we caught a train. Isn't that right, Trixie?" Trixie quickly nodded her assent.

"REALLY?" Twilight almost-shouted incredulously. "So, I'm to assume that the NEW calls for your imprisonment, the bounty on your heads from the Camel Kingdom, and the disabling of half of their Royal Guard was just a figment of our imaginations, then?"

"There are BOUNTIES on our heads?" Trixie seemed almost pleased with that statement, until Starlight smacked her upside the head with her hoof, whereupon she tried to adopt a grave a look as possible, but didn't seem to be succeeding.

"Well, we got taken to see the King," Trixie said, "apparently to congratulate us for putting on a show in the prison, and finally to get to the bottom of why the Cutie Map had even sent us there...as well as clear up the whole pigeon destroying thing..."

"Look, none of us were to know that they spoke Germain..." Starlight started explaining, "and Trixie didn't seem to realise that insulting one's host, REGARDLESS OF LANGUAGE, is both rude and deeply insulting."

"He implied that Trixie's hat deserved to be ruined by that infernal bird of his!"

"And...that led to the new calls for your arrest?" Twilight's anger had briefly been shunted aside in favour of awe on how spectacularly this went wrong, but she found the energy to wind herself back up again.

"Well, we weren't of course going to take it lying down," Trixie said, "and so naturally, we fled."

"We aborted the Friendship Problem and decided to just go home," Starlight shrugged. "Our guest insisted on just packing it in and refused to get involved. So we took 'em and fled out the city..."

"And that somehow resulted in half of the army having to be treated for burns and several broken bones, with insistence that Ponyville foot all the medical bills?" Twilight glared at the pair.

"THAT...was entirely the fault of that puzzle-solving genius," Starlight said.

"And why, exactly, is that?"

"Well, it started when we came across a bridge as we were fleeing from the mob," Trixie chimed in, "and they came up with a rather admittedly brilliant plan of collapsing the bridge while the army were still on it..."

"You did WHAT!?" Twilight shouted.

"I DID say it was all on them," Starlight threw her hooves up. "They stole some of Trixie's leftover fireworks, strapped it to one of the bridge's struts, and timed it to blow at the right moment..."

"By the Elysian Fields..." Twilight felt the urge to down a pint of headache pills at that exact moment. "And you couldn't have just been happy with destroying the bridge to avoid capture...why?"

Starlight and Trixie looked momentarily stunned, as though the idea was seemingly revolutionary. They stared at each other for a good ten seconds, trying to justify such a response, before finally decided to simply be honest. "Extraordinarily petty revenge?"

"OH MY GOSH YOU ABSOLUTE CRETINS."

"How DID that pony know to blow it up at the right time?" Starlight turned to Trixie again.

"Well, Trixie was lacking any form of pocket watch, but luckily, Trixie had two irregular string fuses which burnt after a minute. And they said that was all they needed to time forty-five seconds, which was when every one of the camels was on the bridge..."

Author's Note

This one's too easy, I think, but still.

Two 1 minute fuses.
The fuses are irregular.
You only have one box of matches.

PUZZLE: How can Trixie time 45 seconds?

It Got Worse

"Um...are you alright, Twilight?" Starlight Glimmer looked nervously at the angry twitch in Twilight's eye.

"I'm...FINE..." Twilight growled. She picked up the report again. "And I suppose that you can provide an explanation as to how half of the Camel Kingdom found itself engulfed in flames, requiring the intervention of several of Canterlot's weather team to put out the blaze?"

"Really? First we've heard of it. We didn't exactly stick around for that one," Trixie said, a look of surprise crossing her features.

Starlight thought back to the day of the incident, trying to jog her memory on how the seemingly mostly harmless (save for an entire platoon's worth of broken bones and burns) escape could have escalated... "Wait, I think I know."

"Oh really, DO TELL," Twilight said sarcastically: she'd long since given up on trying to contextualise the colossal screw-up and was simply playing this by sheer apathy mixed with some righteous anger.

"I think some of the sparks from the fireworks caught the grass on the other side..."

"Because OF COURSE IT DID," Twilight shouted. "Of COURSE you three would be responsible for this! Was it all part of your oh so great plan to basically put the entire force into early medical discharge?"

"It was an accident! You can corroborate the story with the other pony...once you...find them," Trixie said, seemingly offended that anypony could be so uncaring. Well, THAT level of uncaring relative to their predicament, anyway.

"According to reports, the fire was blown towards the Kingdom by the winds that were set in place by the weatherponies' machinations earlier that day. The army who had yet to cross the bridge lacked the means to properly control the blaze, and as a result, they were unable to prevent half the city from the blaze until outside help intervened," Twilight replied, narrowing her eyes at the pair. "The fire SHOULD have been cut off at the island since the bridge collapsed due to the weight of the army fleeing from the blaze, and some of them found themselves trapped. But apparently, a stray firework from your...earlier scheme flew towards the kingdom, and ignited several oil cans there. Because OF COURSE IT DID!" Twilight picked up the report again. "Luckily, no lives were lost."

A puzzled look crossed Starlight's face. "Wait, how'd they even escape, then? I'm pretty sure they were stuck on a narrow island, the first bridge we crossed collapsed behind them, and there's sharks in the waters there..."

"How should I know!? I'm already struggling to understand your justification for this entire fiasco as it is!" Twilight gave her most theatrical sigh. "And then what did you do after you had managed to...lose your pursuers?"

"We ran all the way back to the train station, caught the first train back to Ponyville, and we came back to deliver the report," Starlight said, deciding this would be an appropriate time to bring the debacle to an end. She paused. "Wow, the ending sounds pretty lame after all that."

Twilight stared at Starlight and Trixie for a few moments, before declaring, "You two...I cannot even BEGIN to understand how the Cutie Map could have declared this a success. A day that ended in violence, hospitalisation and fire. I have had to spend all DAY trying to clear things up with the Camel Kingdom because of you!"

"Well, maybe there WAS a friendship lesson to be had here," Trixie's voice had taken on a rather foolish tone of optimism.

"And that would be?"

"Sometimes friends need to be reined in before something happens that everypony will regret," Trixie said. "If that horrible bird hadn't just been allowed to poop all over Trixie's belongings, AND that of the prisoners we met, the army would never have been hospitalised, and there wouldn't need to be a fire in the first place."

"That...is not how I would have wanted that lesson to be learnt, honestly..." Twilight groaned. She paced around the office for a bit, before turning on the pair. "You two are to be officially confined to my Castle until I can find your guest and punish them too. You are only to be let out if, Celestia forbid, you are summoned for another Friendship Problem. But if one or both of you screw that one up too..."

"Scout's honour!"

Author's Note

But HOW DID THE REMAINING ARMY SURVIVE?

On an island with no escape.
A raging fire being blown in your direction.

PUZZLE: How can the Camel Royal Guard escape a roasting?

Rock, Rock, Rock (No Fingers, Genius)

Did you know the population of ponies have never heard of Rock Paper Scissors? Unsurprising, given the lack of fingers necessary to play such a truly insightful and fascinating game with such an interesting history.

Alicorns, however, have a special pony-equivalent variation called Hoof, Horn, Wings. A Hoof beats Horn (Twilight Sparkle would object vehemently to the idea of brawn beating brain, but Ogres & Oubliettes players could make a convincing argument otherwise), a Horn wins against Wings by attacking from a distance, and Wings beat Hoof by flying out of reach. Since Alicorns are the only ones with the appendages to play such a game, it's well-known among royalty, and some unicorns who know how to create images with magic, quickly.

Princess Celestia is a particularly big player of the game: you'd be surprised at just how often incredibly big decisions as princess basically boil down to being decided by such a game. But of course, such a simple game of chance invariably gets a bit dull, and so on occasion she does house-rule in another play: the DOUBLE HORN.

It's been said that Bicorns don't exist, but then the same was said of Pinkie's capacity to hold her breath for nearly a day when Trixie rubbed out her mouth and nostrils with the Alicorn Amulet, and she did, just out of spite. Anyway, this special Double Horn that she has introduced adds a twist of thought to such a game. Double Horn defeats Horn, the same way Hoof does, it also beats Wings like regular Horn, and loses to Hoof.

Princess Celestia has always favoured the Best-of-3 approach to these sorts of games, but really, introducing just one new play is hardly going to be mind-blowing: indeed, some may considering it rather unsporting. As a result, Celestia has another rule during any time she house-rules Double Horn in: if at any point regular Horn is played when the opposing pony puts forward Wings, whoever played Horn wins the match, regardless of score.

Of course, hopefully there should never be such a time when you need to pit your wits and/or your neck against her, but it always pays to be crazy prepared for such scenarios. Supposing you were challenged to such a game: there are a number of ways it can play out, so for each phase of the game, how should you approach it to maximise your odds of winning?

Author's Note

This one's going to do several nuts in, I can tell. I won't ask for maths this time, but a general strategy will be...accepted.

Hoof, Horn, Wings is played Best of 3: first to win two rounds, since there can be an infinite number of ties.
Hoof beats Horn, Horn beats Wings, Wings beats Hoof.
Double Horn is added to the mix, which beats Horn and Wings, but loses to Hoof.
If single Horn is played against Wings, whoever played Horn wins the match regardless of score.

PUZZLE: For each possible score (0-0, 0-1, 1-0, and 1-1) what's the most optimal strategy to win the match?

The Culmination Of All, Part 1

It started off as just another ordinary day in Ponyville: you had finally come back from your well-earned vacation and were just about to head to Sugarcube Corner for your regular box of pecan muffins, when suddenly Derpy, the local mailmare, arrives with a letter for you.

The contents are, it has to be said, startling. Not least because you have apparently been summoned directly to Canterlot fro an audience with Princess Celestia herself, but because the matter involves a Friendship Problem, and despite your absolutely ham-hoofed attempt to solve the last one you weren't even supposed to be involved in, the Cutie Map has, oddly, glowed with YOUR Cutie Mark, along with all six residents of the castle, so evidently the Map either has a sense of humour, or it trusts all seven of you not to collectively botch the whole thing.

Regardless, as soon as you have finished reading the letter, Princess Twilight Sparkle teleports right in front of your eyes, but just before you can make to flee for your life, she ropes you back with magic and promptly frog-marches you, with help from her friends, to the train to Canterlot.

It's an awkward ride to Canterlot, as Twilight is reluctant to explain exactly what happened to her friends, and keeps giving you the stink-eye for reasons known only to you and her...nonetheless, it is otherwise uneventful, save for Rainbow Dash pranking the ticket collector, and all seven of you soon find yourselves right inside the throne room of Canterlot Castle.

Princess Celestia explains to you all that there is an national crisis taking place within the Gazelle Plains, but before she elaborates any further, she notices you've apparently been invited along as well. This, perhaps, is a necessary component to see it resolved, but first she would like to test your wits.

Everypony seems a bit confused, but Celestia explains: if you've been called to summon a Friendship problem, you should first demonstrate you have what it takes. She acknowledges your smarts, but she claims that the puzzle she is about to set you will test...more than that. She then points her hoof at you, Rainbow Dash and Applejack, and announces that the three of you will take part in her little test.

She then calls one of the Royal Guards over, and whispers something in his ear. He nods and departs from the chambers. Celestia then tells the remaining ponies to wait, and leads you, Rainbow and Applejack down into the dungeons.

Reassuring you that this isn't for what happened during your vacation, she explains to the three of you the following test:

Down in the dungeon, there are three cells. Each cell has a certain number of apples inside, distributed by the royal Guardspony from earlier, with no fewer than one and no more than nine. No cell contains the same number of apples. Celestia will now guide each pony to a cell, where they can see the number of apples inside, but they will not be allowed to view the contents of another pony's cell.

Celestia will now allow each of you to ask her one question, to which the answer is either yes or no. She will answer truthfully to each one, and you must now work out how many apples there are in total in the three cells. A correct answer from one of you would see all three of you pass the test.

As you are being guided to your own cell, Rainbow raises her hoof, asking what's to stop all three of you from just looking in their cells, forcing her to clarify the apples inside by asking "Are there -blank- apples in my cell?" and just passing the test that way,to which Celestia replies, what a good idea: let's not allow you to do that. Smooth move, Rainbow.

So with that question out, she says Applejack will ask first, then Rainbow Dash, and then you. Certainly wanting not to fail, Applejack decides to lead by asking whether if the total number of apples is an odd number, to which Celestia replies yes.

Rainbow then asks whether if the total number of apples is a prime number. She sounds a little proud of herself for knowing about numbers that can't be divided exactly except by themselves, and one: probably trying to impress you. Celestia replies no.

Now it's your turn to ask. You turn to face your cell, and you can see five apples total inside.

You have everything you need, but what, exactly, did Celestia mean by the puzzle testing more than just your wits...? What should you ask Celestia to pass?

Author's Note

So, this is it. The final stretch. Pass Princess Celestia's test and you earn the right to accompany them to this Friendship Problem.

You, Rainbow Dash and Applejack placed in separate cells.
No two cells have the same number of apples.
There are no fewer than one apples, nor greater than nine apples in a cell.
You can count the number of apples in your own cell, but not anypony else's.
You have five apples in your own cell.
Each of you are allowed one Yes or No question each, which Celestia will answer truthfully.
Applejack: Is the total number of apples an odd number? Princess Celestia: Yes.
Rainbow Dash: Is the total number of apples a prime number? Princess Celestia: No.

PUZZLE: What should you ask Princess Celestia?

The Answer 38

"Are there fifteen total apples in the cell?"

How long did it take you to realise it? Perhaps a more self-reliant pony would try to think of a question that would allow them, and ONLY them, to solve this puzzle. But if you're being called to solve a Friendship Problem, you need to trust in others to see a puzzle solved, and that means finding a question that will allow at least one of you the means to guess the number.

Since we know we cannot have empty cells, nor cells with the same two amounts of apples, the lowest number of apples we can have is six (1, 2 and 3) and the largest total is twenty-four (7, 8 and 9).

From Applejack's first question, we know there are an odd number of apples, and Rainbow Dash's question revealed it isn't a prime number. Eliminating all even numbers plus prime numbers only leaves us with three possible totals: nine, fifteen, and twenty-one.

So if you asked the above question, here's how things could play out:

1.1 If the answer is yes, great! Any one of you can guess the answer is fifteen.
2.1 If the answer is no, then there are either nine apples, or twenty-one. Seeing that your cell has five apples, you know that one cell has three apples, while another has one. Assuming both Rainbow Dash and Applejack are following logic, whoever can see only one apple in their cell must deduce that there are nine apples, since you can only have a maximum of eighteen apples with one cell holding a single apple. Meanwhile, whoever can see three apples knows there can only be a maximum of twenty apples, so they too must deduce there are nine apples.
2.2 In the event there are twenty-one apples, following similar logic, one cell will have nine apples, the other will have seven. They should then deduce that there are more than nine apples between the three cells and thus conclude there are twenty-one apples in total.

The Culmination Of All, Part 2

Satisfied, Princess Celestia nods her head. The question she was looking for was one where you trusted another friend to come to the answer to her puzzle: trust is key.

She leads the three of you back to the throne room to announce that you have passed, to the relief of the remaining ponies. She then explains what is going on.

Recently, Canterlot has received an unprecedented number of foreigners directly from the Gazelle Plains, which was apparently in response to a deadly disease that had gripped the land - a terrible virus known as Geo-orgosis. Sufferers of the disease show no external symptoms until a few moments before their body suddenly crystallizes into a solid mass resembling hard diamond, and the only way they know they have the virus is a very strange feeling inside...

It is believed that the gazelles carrying the virus were exiled from their home and quarantined in Canterlot - without permission from Celestia or Luna. And since Canterlot isn't really prepared for such a sudden population increase nor the sheer paperwork necessary to try and either send them back or keep them, they are sending the seven of you directly to the Gazelle Plains to try and ascertain the situation and resolve it. She adds that she has faith in Twilight's anti-biohazard spell and recommends casting it on you all before you leave.

You then catch the next airship to the Gazelle Plains (and this time Rainbow Dash doesn't need to queue up behind 499 other ponies to get on) and you are whisked away to the lands directly neighbouring Zecora's Zebra Lands...

Upon your arrival, all seems perfectly normal. Twilight then recommends that everypony try and get a feel of the place before trying to speak with the higher ups - but as she does, she sees a nearby male gazelle unfortunately increase his own bodily density by several times by inconveniently crystallizing himself. Twilight only manages to freeze the process enough to allow his face to remain intact, where he admits a shocking truth: there are many more gazelles with the disease, but aren't coming forward out of fear of spending their final few weeks in exile. Unfortunately, that is all he can manage before the spell breaks and he becomes a rather handsome garden ornament.

Realising that this needs to be taken up with the rulers of the Plains, they quickly borrow several tourist maps and frantically make their way towards the Plain Palace (which, as they discover, certainly is an appropriate name, in more ways than one: it's a solid grey). They quickly barge into the palace and demand to see whoever's in charge. It takes Twilight Sparkle flashing some sort of very shiny badge and a lot of titles being thrown around on the part of Twilight before you're finally granted an audience.

You are then taken to the Supreme Leader: a gazelle wearing rather thorny and rather dangerous attire, including a literal crown of thorns, causing Rarity to wonder how it doesn't just catch in the fur or mane, where Twilight explains Canterlot's sudden population increase.

The Supreme Leader concedes that it was unfortunate on the part of the ponies, but he was left with no recourse: it was the only way to contain the outbreak of Geo-orgosis. And it evidently worked: since then, the number of gazelles admitting they had the virus dropped to precisely zero. Applejack then points out the gazelle they saw that got the authentic cockatrice experience, but he laughs it off, and Pinkie and Rarity have to restrain Rainbow Dash from punching him in the face and/or yelling at him.

Twilight asks if they are at least working on a cure, but the Supreme Leader doesn't see the need for it, given how the problem was 'solved'. But he does concede he could be wrong and that it's worse than he thought - but only if you can prove it. Only if the seven of you can prove the disease is still rampant will he and his best doctors sink the money into a cure. However, suspicious of how the ponies have a vested interest in ridding themselves of any illegal immigrants, he says that he will not accept any secret ballots, or anything that doesn't provide the names of the surveyed gazelles along with their entries/answers. Furthermore, he must be able to contact every gazelle to confirm they answered exactly as recorded, to avoid any falsehoods and fake news.

After finding themselves outside the palace, the seven of you try to brainstorm some ideas. Fluttershy is certain everyone who has Geo-orgosis knows that they have it, and Applejack is certain that they would all understand the importance of the survey and tell the truth. However, it is pointed out by Pinkie that no-one is willing to own up to having Geo-orgosis or else they get a one-way trip to Canterlot, and starts trying to devise some sort of secret code, but Rarity reminds everypony that codes can't be allowed - the Supreme Leader's government said no secret answers.

Everypony seems completely stuck for ideas, until the six of them turn their heads to you for YOUR opinion. They are all clearly in a quandary. How CAN the seven of you survey the population, accurately establish the spread of Geo-orgosis, and get all who have the disease to admit to it, while making sure no-one can ever use the information against them?

It's up to you to take everything you learned so far and try to find the answer and make sure the entire Gazelle Plains doesn't becomes populated with lumps of biological rock!

Author's Note

So, I guess this is the final puzzle. I had others lined up, but little ways to contextualise them. Perhaps, another day...another series...

But have fun with this one. If you manage to solve it, I'll even upload the remaining missing answers. So have at thee.

Everyone who has Geo-orgosis knows that they have it.
Everyone understands the importance of telling the truth.
Your survey must not contain any information that can tie an individual as to whether or not they have Geo-orgosis. Writing down the answers in code or locking them away is not enough: there must be NO information in an individual's answer.
Your survey must reflect, to a reasonable degree of accuracy, how far the epidemic has spread.
You cannot survey anonymously.

PUZZLE: How should the survey be conducted and data collected?

The Answer 39

The first thing that should become obvious is that there generally won't be a single question that will satisfy the criteria of an accurate survey, non-anonymously carried out, that gets a gazelle to confess they have Geo-orgosis, while also containing no information that proves they have it. So you realise it must be a two-step process.

You should also realise that it is impossible to avoid asking at least one gazelle if they have the virus.

It therefore sounds impossible, since no-one can be surveyed anonymously. But there IS a loophole. While it's true you cannot keep the answer a secret...the real genius lies in the realisation that what needs to be kept secret is the QUESTION.

And the best way to that is to ask one of two questions, and leave it up to chance regarding which one gets asked, to create plausible deniability for the surveyed gazelles. So let's introduce a random element, such as tossing a coin.

Get your surveyed gazelle to toss a coin. If heads, ask if they have Geo-orgosis. If tails, get them to toss the coin again, and ask "Did you get heads on your second toss?"
Regardless of whatever was asked, divide all answers into yes's and no's (with names written alongside each answer of course). Since a binary yes or no is all that is being recorded, the government, if suspicious, can easily contact them and verify they answered truthfully, without them actually knowing what it was they were being asked.
Maths time!

Let's say we surveyed 1000 gazelles and got 450 yes's and 550 no's. The odds of a coin flip is 50:50, so give or take a margin of chance, 50% of the gazelles will not have been asked if they have the virus, and so got asked if they got heads on the second toss. And the odds of getting heads again is also 50:50, so those who got asked the other question should, give or take, return with 250 yes's and 250 no's.

We then deduct that from the main pile to get 200 yes's and 300 no's, to represent those who got asked if they have Geo-orgosis. But that's only half the surveyed population, so we double this, to 400 yes's and 600 no's.

As always, like any good survey, the larger your sample size, the more accurate and reliable your end results will be.

So we have our accurate survey of how far the virus spread, a record of everyone's answer, and nothing to suggest to the government that they have the virus.

The Answer 6

Daring Do obviously couldn't move in a straight line all the time or else the gremlin would just catch her. She therefore started headed towards the edge...but then started to move in circles, gradually making the circle bigger.

Small circles have a small circumference, less than that of a quarter of the sigil's circumference, and so the gremlin slowly fell behind tracking Daring's movements. The trick was to keep the circle small enough that the gremlin was still falling behind.

Daring knew she was four times slower than the gremlin, so the biggest circle she could make was one where the circumference was just less than a quarter of the sigil's circumference (pi times diameter, in other words, 3.14 x 30m, equalling 94.2m). She therefore made a circle of a 23.5m circumference (she rounded down from 23.55 to ensure the gremlin kept falling behind), with a radius of 3.74m, going by the formula r = c/pi/2.

After making this circle of a 3.74m radius, Daring was now 11.26m away from the outside of the sigil and freedom, so she just made a straight dash for it. Were she four times faster, she could cover 45.04m in the time it would take the gremlin to catch her. Unfortunately for the gremlin, the fastest route to her was still half the sigil's circumference, which was 47.1m! He simply couldn't cover that distance in the time it took Daring to run 11.26m.

Once again, our statistically improbable heroine escaped another trap!

The Poison Apple Joke Cider

Cider Season was considered to be one of the highlights of living in Ponyville. There wasn't a whole lot else to look forward to, living in a small town in the country. The odd monster or evil villain invading the town did shake things up, but at least the place didn't have to deal with traffic. And every invasion did at least let the citizens get good exercise from all the running and screaming. And the community picnics as they repaired the town were always excellent.

It was during one such Cider Season that Twilight Sparkle, Princess of Friendship, and her old student, Starlight Glimmer, were making their way to Sweet Apple Acres Orchard. This was rather worrying for the pair: the orchard opened for Cider Season in an hour and ten minutes, but Applejack, one of the owners and Twilight's long-time friend, had called them over, claiming that she had an 'awfully big doozie', and that she was hoping the two of them could think of some sort of solution by the time it was time to open up for the locals.

"So what does Rainbow Dash see in it, anyway?" said Starlight as they were walking, "I've never actually tried it for myself. I missed the last one."

"Well, Rainbow says that the taste is to die for," Twilight replied. "I personally think it's best shared with friends. Since, you know, if you just have it by yourself, that's when you need help, if you know what I mean."

"I don't know what you mean," Starlight said, blankly.

"Oh. Well, ask Rainbow. ask about that time she did somersaults after four mugs. I think she still remembers that despite everything." Just then, Twilight turned her head back forwards, and spotted the outline of an orange pony wearing a brown stetson hat. "Oh! There's Applejack!" She waved her hooves at their friend.

The pair trotted up to the farmpony. She looked somewhat tired, as if she had stayed up all night thinking about the problems with the world. Of course, Sweet Apple Acres pretty much WAS Applejack's world, so Twilight figured the analogy wasn't that far off.

Starlight spoke first. "Hey Applejack. You look terrible, no offense."

"Ah FEEL terrible," Applejack sighed. "Cider Season's comin' up any moment and this had to happen of all times..."

"What is it, anyway?" Twilight said, the concern evident in her voice. "Pests, or something like that?"

"If only. That'd actually be easier to deal with." Applejack shook her head. "Nah, Ah'm all wound up 'cos some no-good snake slipped some Poison Joke into one of our cider barrels right before we were done countin' 'em!"

"They did?" Twilight gasped. She was all too familiar with the effects of the flower that grew inside the Everfree Forest, with that plant having once caused her horn to flop over like a limp, wet towel several years ago. "But Poison Joke extract is said to be odourless, AND tasteless, and it acts within forty-five minutes of contact..."

"Don't Ah know it," Applejack sighed. "And we don't know which one it is, so as y'all can see, that leaves us in a bit of a bind. We'd be putting out that cider and some of the guests could end up with all sorts'a awful headaches."

"Geez, who would even do something like that?" Starlight wondered.

"Dunno. Some joker who's trying to shoehorn in a mystery to solve for attention at the most dramatic or convenient moment. Or a friendship lesson in the makin'. We get those. A lot."

"How many barrels of cider DO you have?" Twilight asked.

"Two thousand."

"Two thou-" Both Twilight and Starlight's eyes boggled at the thought. "Okay, you don't have that many working there and Sweet Apple Acres isn't THAT big! How did you even-?"

"Family from all over had leftovers they didn't shift," Applejack replied. "So they figured Ah should have 'em. We know how much Ponyville loves the stuff. Especially Rainbow, Ah swear she'd replace all the water for clouds with cider if anypony let her."

Twilight was dumbfounded. "So...you have two thousand kegs of cider, one of which was laced with Poison joke extract, and you don't know which one. That's the gist of it." She shook her head. "Well, you can't risk the customers waking up with a horrible condition, I'm pretty sure Zecora can't supply cures for THAT many ponies. You'll just have to dispose of it as waste."

"Twi, Ah can't just throw out ALL the cider we have!" protested Applejack. "Do ya realise how much of a loss we'd make? We'd struggle to get back on our hooves in time for next year!"

"Well, what else is there!?" Twilight shot back. "You can't just serve all this knowing it's tainted!"

"Or..." Starlight mused out loud, "...we just get some guinea pigs to test each batch before you open for Cider Season."

Twilight and Applejack both glared at Starlight. Twilight was eyeing up the unicorn with a look that would surely have reduced her to a fine, burnable, explosive power if looks could rob lives. Applejack's glare was less intense, which Starlight attributed to the thought of less of a financial burn in the pocket, but it was still as angry as a business-pony could manage while still seeming sincere.

Starlight threw up her hooves. "It'll be for the greater good!"

"Starlight, that is utterly horrible!" Twilight shrieked.

"More horrible than Sweet Apple Acres taking a massive financial hit and leaving all those unhappy patrons high and dry?" Starlight replied, raising an eyebrow. "And yes, the 'high and dry' bit was intentional, thanks."

"You're still proposing throwing victims to the timberwolves!"

"Yeah, but at least they'd KNOW about it," pointed out Starlight. "And we'll compensate them afterwards!"

"Who's this 'we'?"

"Well by that, I mean you two, since, you know, you have money. Well, so do I, but I don't exactly have a JOB job..."

"Starlight..." growled Twilight.

"Not that it ain't sort of a kick to the teeth to these ponies," said Applejack with a great degree of skepticism, "but who are you gonna get to go through all two thousand barrels AND have their dignity robbed until Zecora can patch 'em up?"

"Not that many, if I've got this right," smirked Starlight. "Sit tight, I'll be back!" And she promptly galloped away.

"Should Ah be worried?" Applejack asked Twilight, as they watched Starlight melt into the distance.

"Probably," was the nervous reply.

"And how many ponies are we goin' to have to apologise to by tomorrow? She DOES intend to keep the casualties as low as possible, right?"

"Hopefully," Twilight sighed.

Author's Note

Hey guys. So what can I say, I found myself in the mood for puzzles one day and my fevered brain came up with this.

So here it is. The first puzzle. For those of you who need to keep track of the clues (or just didn't read it, cheers BTW), here's what you work with:

2000 barrels of Sweet Apple Acres Cider.
One of the bottle is poisoned with Poison Joke.
Poison Joke acts within 45 minutes of contact.
You have 1 hour to find the poisoned barrel.

PUZZLE: What is the lowest number of pony guinea-pigs Twilight, Starlight and Applejack need to find the poisoned barrel within the time limit?

The Answer 1

It would take 11 ponies to go through all 2000 barrels.

First, you number all 2000 barrels from 1-2000. Then you assign each barrel a unique combination of testers to sample them.

In a simpler scenario with 4 barrels, you only need 2 testers, with each one testing each barrel as follows:

Nopony sups from Barrel 1.

Tester 1 sups from Barrel 2.

Tester 2 sups from Barrel 3.

Testers 1 and 2 sup from Barrel 4.

If they're both fine, Barrel 1 is the infected one. If only Tester 1 gets poisoned, it's Barrel 2 that's infected. If only Tester 2 gets pranked by the plant, it's Barrel 3. And if both testers get hit with Poison Joke, it's Barrel 4.

Working downwards, to test all 2000 barrels, the lowest number of ponies required is 11, for 2048 different combinations of testing. n testers requiring 2n combinations.

If You Don't Like Broccoli And Hazelnut Cupcakes, Tirek Wins

Howdy there, friend! Your friendly neighborhood Pinkie Pie here! Welcome to Sugarcube Corner!

Oh, you're here for the usual pecan muffins?

Not today? Oh...well, if you're in the mood to try something new, I finally perfected my recipe for broccoli and hazelnut cupcakes?

What's that? You've never heard of them? *GASP* Oh, dear sweet thing, if you haven't tried my broccoli hazelnut cupcakes then you haven't LIVED, baby! LIVED I SAY!

I've got some of the spare batter in the kitchen right now! Just give me fifteen minutes!

...

...um, Houston, we have a problem.

Oh, don't ask who Houston even is, I don't know either! But it's a catchy thing to say, right?

See, these cupcakes need eleven minutes to bake. I have to crank the heat up SUPER high for the best results. That super crunchy bite with the right amount of sweet and bitter...that, filly, is art! If art was delicious.

Well, if you're asking if I have a timer...Mr and Mrs Cake are borrowing it right now. And the clock's still at the menders.

But I DO have...(hang on, they're in my mane somewhere...ah, there we go) ...a pair of hourglasses that I stash away in case of hourglass emergencies! But I mean, really? I somehow haven't hidden away any timers in case of timer emergencies? I swear I'd forget my head if it wasn't screwed on, except if my head WASN'T screwed on then it'd fall off and I couldn't breathe or eat or snore or belch or yodel or-

Oh yeah. Cupcakes. And the lack thereof.

But anyway, they need eleven minutes in the oven and all I have are these. Have you got a watch?

No? Well, worth a try!

Author's Note

Right. Shouldn't be too difficult. In theory.

You have a five-minute hourglass and an eight-minute hourglass.
No other timing equipment available.

PUZZLE: How can PInkie measure eleven minutes?

The Art Of Business (And Unlikely Logic)

One night, there was a sudden storm blowing over the Everfree Forest, which resulted in several of the ducks living at Fluttershy's cottage to misplace their ducklings: using the word 'lost' would imply they'd never get found again. And as brave as Fluttershy was (which is to say generally never), there was still a limit to her tracking skills. As it turned out though, she happened to see an advert in Equestria Daily yesterday for an animal rescuer from the Minotaur Lands, and decides that she's got nothing to lose apart from a service fee for trying.

As it turns out, the rescuer was a rather old but surprisingly buff guy, who looked as though he'd picked a fight with about seven hydras all at once and lost. Despite the fact that he only had one good eye and was apparently deaf in the left ear, assured Fluttershy that he can track and retrieve all sixty-three ducklings that went missing. With the job clarified, the rescuer went on to discuss the matter of payment.

Unfortunately, all of Fluttershy's spare bits was allocated to looking after the rest of her animal critters, and so she was left with no choice but to pay in collateral. As it happened, she had a gold chain necklace made up of (by a frankly contrived coincidence) sixty-three links. She decided to part with that, but owing to the disproportionate value of the chain, Fluttershy refused to pay up front. The animal rescuer, however, suspicious of Princess Celestia's foreign policy and of ponies in general, wouldn't take a payment afterwards in the event of Fluttershy reneging on the deal.

Fortunately, as any good friend can tell you, a compromise solves everything. They agree that Fluttershy will pay the rescuer one link for every successful rescue, protecting both from foul play. Unfortunately, it IS a rather pretty necklace and the minotaur doesn't want it ruined beyond repair, so he demands Fluttershy make no more than three breaks in the chain.

Completely stymied, Fluttershy now needs you to sort out this problem. And maybe learn some sort of lesson in friendship if it turns out there is one.

Author's Note

You have a sixty-three link straight golden chain.
You cannot break any more than three links in the chain.

PUZZLE: How can Fluttershy pay one link per rescued duckling until all sixty-three are safe, without breaking the chain more than three times?

The Answer 11

Did you draw out a grid and start tracing routes? Well, you're on the right track, but as Shining Armor found, it's not possible to visit each room only once without missing one.

This catches some ponies out because it IS true that any contaminated room you visit must be destroyed before you leave. But that's just a case of not reading the question carefully. Isn't there one room that isn't contaminated, and thus fair game to visit more than once?

That's right: the entrance. It's the only uncorrupted room.

True, Shining WILL have to destroy the entrance after his second visit to keep the dark magic from spreading any further, but one more visit is all he needs.

Now that you know you need to double back to the entrance to solve the puzzle, you will find there are at least 8 different ways to solve this puzzle: 4 starting by destroying the room south of the entrance, and 4 involve destroying the room east of the entrance first.

Can you find them all?

The Answer 12

If you knew if the twelfth coin was lighter or heavier, this would be easier. But you don't, so...

Number each coin 1-12. Split the coins into groups of four numerically, then take group 1234 and weigh it against 5678.

IF FIRST WEIGHING BALANCES:

1.1 Now you know one of the coins you didn't weigh is the one you're looking for. Remove all coins except coin 8, then weigh 9 and 10 against 11 and 8.

IF THEY BALANCE AGAIN:

1.1.1 Great! You've weighed 11 coins and they're all equal, ergo the twelfth un-weighed coin is the one you seek.

IF THEY ARE NOT BALANCED:

1.1.2 In the event side 9 and 10 is lighter than 11 and 8, either 11 is heavier than the others, or either 9 or 10 is lighter than the others. So weigh 9 against 10. If they balance, it means 11 is heavier. If not, you know that either 9 or 10 is lighter than the others, so the lighter coin must be the different one.

1.1.3 But if side 9 and 10 is heavier than side 11 and 8, same logic applies. Either 11 is lighter or 9 or 10 is heavier. Weigh 9 against 10. If they balance, 11's the one. If not, the heavier coin is the different one.

IF FIRST WEIGHING IS NOT BALANCED:

1.2 In the event side 1234 is lighter than 5678, it means either 1234 is lighter or 5678 is heavier. So take coin 9 and weigh 1, 2 and 5 against 3, 6 and 9.

1.2.1 If they balance, either 4 is light or 7 or 8 is heavy. You then simply weigh 7 and 8, and if they balance, 4 is light. If not, the heavier coin is the one.

1.2.2. If (when we weigh 1,2, and 5 against 3,6 and 9) the right side is heavier, then either 6 is heavy or 1 is light or 2 is light. By weighing 1 against 2 the solution is obtained.

1.2.3. If (when we weigh 1,2, and 5 against 3, 6 and 9) the right side is lighter, then either 3 is light or 5 is heavy. By weighing 3 against a good coin the solution is easily arrived at.

1.3 If (at the first weighing) coins 1,2,3,4 are heavier than coins 5,6,7,8 then repeat the previous steps 1.2 through 1.2.3 but switch the numbers of coins 1,2,3,4 with 5,6,7,8.

Mo' Money, Mo' Rocks, Maud Pie

So you're the hired hoof?

Hello. I'm Maud. Maud Pie. You're working with me today.

I know you. Pinkie told me.

What are we doing? We're farming inexplicablyvalumium.

Inexplicablyvalumium. It's a rare mineral. We can only find it in about 1% of the rocks on the farm.

We need to check all our fields for it.

It won't be as hard as you think. I have a secret weapon.

I have a special inexplicablyvalumium detector. It beeps when it finds any.

I worked on it for months.

Hmm? Oh, it's not that simple. It's not perfect.

About 10% of the time it'll beep, even when there is no inexplicablyvalumium.

But it's still reliable enough for us. Until I perfect it, anyway.

You'll get used to saying it. Now, when it beeps, load the rock into the cart and we'll take it back to the farm to be examined. Okay?

Good.

Thanks for all the work today. That's a big one.

...

...Say. Do you want it? I'll sell it to you.

How much? 20,000 bits.

A rock of inexplicablyvalumium that size can fetch 100,000 bits.

You'd be getting it for a fifth of the price.

Not bad, is it?

What do you say?

Author's Note

The answer's Just a stone's throw away. Just to be clear though, I won't accept a binary yes or no answer: I'll only upload it if you can explain why as well.

1% of the rocks on the rock farm contain inexplicablyvalumium.
Maud has a detector that will always detect inexplicablyvalumium if it is present.
If a rock doesn't contain inexplicablyvalumium, it will give correct readings 90% of the time.
Maud offers you 20,000 bits for a rock you farmed that could be worth 100,000 bits if it's genuine.

PUZZLE: Should you take the deal?

The Answer 17

Rainbow Dash has a 50% chance of sitting in her seat.

To explain, let's simplify things. Suppose Old Oak and Rainbow Dash were the only passengers and there were only two seats. If Old Oak chooses to sit in a random one, there's a 50:50 chance Rainbow'll get her seat. No duh.

What if we introduced another passenger? Well, assuming Old Oak randomly sits in the seat of this third passenger, they are forced to choose between either Old Oak's seat, or Rainbow Dash's. As we're only considering 'the odds that Rainbow Dash will get her seat', this is still a 50% chance Rainbow will have to sit in Old Oak's unclaimed seat.

Using recursive logic, we know that in the case of 500 passengers, the odds are, surprisingly, exactly the same. Old Oak randomly sitting anywhere else only postpones the decision: it doesn't affect the odds at all!

Still confused? Say Old Oak randomly sits in seat 212. Passengers 2 to 211 will sit in their correct seats. Now it comes to the 212th passenger, and one of three things could happen:

They randomly sit in Old Oak's seat.
They randomly sit in Rainbow Dash's seat.
They randomly sit elsewhere and the decision is postponed still further.

Let's say this random passenger sits in seat 479. Now we continue on with all passengers sitting in their correct seats until the 479th passenger lines up and does one of the three actions.

Assuming nopony randomly sits in Old Oak's seat or Rainbow's, this pattern will repeat for all passengers until passenger 499 is stuck with picking either Old Oak's unclaimed seat, or Rainbow's.

Rainbow Dash can ONLY sit in Old Oak's seat, or hers. There is no other possible outcome. This is like tossing a coin: you can put off the coin flip, but not forever. You'll have to face the 50:50 odds sooner or later!

The Answer 19

This one's a stumper. Actually, the solution isn't as simple as "Twilight deduced there would be no visit, therefore any visit would be a surprise", because that assumes Twilight's logic was correct, and we're being told to explain the flaw in it. The reason is because this creates a paradox.

Imagine Celestia failed to show up Monday to Thursday. Twilight waits for Celestia...and now one of two things could happen. If she was visited on that Friday, then it would mean Celestia's statement about it being a surprise is untrue. Or if she never showed up, it means the part about visiting is a lie.

It's a paradox because they can't BOTH be true.

Twilight's entire chain of logic breaks down at the very last day. Any result then would be self-contradictory, so any logic drawn from them is utterly pointless.

But as long as it doesn't actually GET to Friday, Princess Celestia's statement still holds true. She just needs to visit Twilight by Thursday.

Funny thing though? Nopony could ever agree unanimously what the actual flaw in the logic is. This is just one interpretation Celestia ran with, knowing Twilight so well. Looks like there is still much to learn about being a Princess of Friendship yet!

Is It Called A Bucket Because That's What Ponies Say After Rage-Quitting?

Who am I? I'm Zecora. A pleasure, I am sure.
You claim that around Ponyville, you've not seen me before?

I guess that's understandable. My hut's a bit out the way,
I'm visiting the town for official business, I'd say.

You are perhaps acquainted with the one called Pinkie Pie?
If that is so, perhaps you could indulge me? You ask why?

Rumours of your puzzle skills have reached the Everfree,
And your impressive logic, I would rather like to see.

I therefore challenge you to find the answer to my puzzle,
If you're as good as ponies say, this will not leave you muzzled?

I have right here in front of me a bucket filled with potion,
And I do seek to challenge you with quite a curious notion.

The bucket has no markings to determine just how much,
How do you find this out? Not by guessing, not as such.

I filled it to the halfway point to the best of my ability,
But chances are I'm slightly off, speaking of practicality.

It could be slightly fuller, perhaps emptier instead,
Or it may be filled exactly, putting me already ahead.

Using the bucket only, however can you tell
Just how much potion's in there? I hope the answer's well!

Author's Note

Probably not.

One cylinder-shaped bucket of potion.
You know it's close to being half-full, but not whether if it's more, less or exactly right.
The bucket has no markings to measure the amount.

PUZZLE: Using ONLY the bucket of potion, how can you tell how full it really is?

The Answer 25

You can find the three fastest cadets in seven races.

The first five are spent racing all the cadets once each, five at a time. Keep the top three finishers for each race and eliminate the bottom two, since a pony who came fourth or below can't be the THIRD-fastest. That eliminates ten possible cadets.

Next, run a sixth race, composed of the winners of each previous race. Whoever wins this one is the fastest cadet, so you can safely put that cadet to one side. Keep the second and third place finishers and eliminate the bottom two.

This is the part that Spitfire mentioned: some of these cadets will already have proven to be unable to make top three overall, and are going to be dropped. Next, go through everypony who lost to whoever came third, fourth and fifth in the second heat during their first heats and eliminate them. That leaves only six cadets in the running.

One other cadet can also be eliminated: whoever raced the pony who came second during the second heat, but came third during that first heat, since you now know at least three other ponies faster than that cadet. So you're left with only five ponies.

Finally, have them race, and whoever makes it to the top two are your second and third-fastest cadets.

The Answer 26

Sounds impossible, doesn't it? If Rarity is going to fall behind by a second every mile, how can she ever catch up? But of course, there MUST be a way, or else we wouldn't have this puzzle.

First, think about how Rarity can run at different speeds, yet cover every mile in the same amount of time. She does this by sprinting for the first part of a mile, then jogging for the rest of it. Repeat for every mile: basically, she runs x of every mile, then jogs for the remainder.

Let's adapt the strategy to suit Rarity's needs. The race is 26.2 miles long. So if she loses a second every mile, after 26 miles she'll be 26 seconds behind, so we need to make up 26 seconds in 0.2 miles.

Make the strategy so that Rarity should run 0.2 miles at top speed, then jog for the rest of the mile.

Let x + y = 8 min, 1 sec, or 481 seconds. The important thing here is to focus on time, not distance. If Steady Pace runs at the constant speed of a mile every eight minutes, he's expected to finish a 26.2 mile marathon in 12,576 seconds (when you convert the minutes). So to beat him, even by a hair, we need to run this race in 12,575 seconds.

Rarity will be running the 0.2 mile cycle 27 times, and the remainder only 26 times, so plugged into a formula, we get:

27x +26y = 12,575. Our previous formula shows that y = 481 - x, so we sub y with that, and happily, we can cancel it down, resulting in x = 69 seconds, and y = 412 seconds.

So if Rarity sprints 0.2 miles in 69 seconds, and the remaining mile in 412 seconds, she'll lose every mile versus mile comparison, but the final 0.2 mile sprint should allow Rarity to just catch Steady Pace and win!

The Answer 30

As Rainbow definitely knows she isn't possessed, she can explore one of the corridors alone. The problem is figuring out how to divide the rest of them.

Let's imagine you decide to send at least one group of four down one of the paths. That's a no-go, because what happens if they come back and they're in disagreement over where the exit is? If they're evenly split, then you'd have to guess who's lying and who's telling the truth.

But sending Rainbow, a pair and two groups of three down the four paths WOULD work.

When you come back to the room to report, you just listen to each group (assuming Rainbow doesn't find the exit herself). The groups will either give the same report over whether they found the exit, or there will be an argument breaking out. Now, one of three things can happen:

If nopony in the group is arguing over the exit's location, it means either everypony is telling the truth, or you've paired the possessed students together. In either case, ignore the duo and go with whatever the groups of three are saying. This will of course only give you reliable information on three of the exits, but that's fine, since you can figure out the safe one through process of elimination.
If only one of the groups is arguing, it must mean the remaining groups are telling the truth.
If two groups are arguing, you know that you've split the possessed students into two groups. Even then, since you know that you can ignore what an arguing pair is saying, it's still safe to trust the majority of a group of three, since you know that there can only ever be one liar in each group.

Good thing Rainbow heard about this puzzle from one of the Daring Do books, eh?

The Answer 32

Since we're eliminating the more lateral solutions by removing the option to get others involved in this little scheme, including the messy side of the legal system, and we can't threaten the bank manager, the solution is to get this one solved mathematically.

Lyra has the puzzle's solution on-hoof, coloured in three colours (let's say red, blue and yellow). What she needs to do is have ANOTHER copy of the puzzle's solution, in different colours (for example, green, purple and orange). She should then cover up that map and ask Tender Lender to choose two adjacent areas of the map. She then reveals that the two parts are indeed in different colours.

Depending on how skeptical Tender Lender is, Lyra could be there for a while. If the map were made up off one hundred shaded parts as an example, if Lyra actually doesn't have the solution, at least one area of the puzzle will have two areas shaded in the same colour, and thus a 1% chance of being caught out. So after the first reveal, Tender Lender can at least be 1% sure the solution is real.

Lyra should then repeat the above highlighted steps again, changing colours every time (in case Tender Lender has an exceptional memory), including making the copy of the solution and redoing it again. Repeat until Tender Lender is convinced. If Lyra has an incomplete solution, the more this is repeated and she isn't caught, the likelihood of a lie plummets to negligible levels, if it were completed save for one border.

This sort of solution is an example of zero-knowledge proof, for those of you nerdy enough to try and look it up: a way to prove you know a thing without any proof except the fact you know the thing.

The Answer 35

To cut the burning time in half, the fuses need to be lit at both ends.

Light both ends of one fuse, and only one end of the other fuse at the same time. It will take thirty seconds for the fuse lit at both ends to burn up. (30 seconds)
Once it's burnt up, light the other end of the remaining fuse.
You have 30 seconds worth of fuse, and now you've lit the other end it takes 15 seconds to burn through. (45 seconds)

The Answer 36

With a huge fire blowing their way, the army were forced to fight fire with fire, by starting ANOTHER series of fires, perpendicular to the wind's direction and downwind of the first fire.

This new fire then burned all the vegetation right behind them, and they simply walked on the charred path as it burned through the rest of the island...and towards the kingdom because of the sparks from THAT fire, but...

Anyway, the first fire then had nothing to sustain itself, and it died out.

The Answer 37

0-0: Favour Hoof, which wins 52% of the time, compared to Double Horn (0%), Horn (24%) and Wings (24%).
0-1: Favour Hoof, which wins 55% of the time, compared to Double Horn (0%), Horn (21%) and Wings (25%).
1-0: Favour Hoof, which wins 40% of the time, compared to Double Horn (33%) and Wings (27%).
1-1: Randomise equally between Hoof, Wings and Double Horn.

When you're playing a regular game of Hoof, Horn, Wings, you should randomise equally between the three with equal probability, because any other strategy will be exploited by a savvy opponent: if, for example, you favour Wings, the opponent will know to play Horn and you will lose in the long run.

A similar train of thought applies here. First off though, you should probably have noticed that Double Horn basically is Horn except better, for all intents and purposes when you're in the lead. After one win, it's never optimal to use just Horn again: there's no reason not to use what is effectively Horn with more win-conditions when you have one win in the bag, and you won't benefit from single Horn's insta-win condition at this point. So when you're tying 1-1, you cycle between Hoof, Double Horn, and Wings with equal probability.

What if you're winning 1-0? Smart opponents will definitely know that it's now a contest of Hoof, Double Horn and Wings, because Horn is a strictly dominated strategy for you. They will then pick from the four options, as usual.

If you play Double Horn against Horn or Wings, you win. If you play Wings against Horn, you lose the match thanks to the insta-win con. Let's call the probability of winning the entire match X. X is 1 if you win this round, and 0 if you play Wings against Horn. And of course, if you're 1-0 up and the opponent instead wins with anything that isn't Horn, it's 1-1 and the odds of winning are 50%, assuming you're both playing optimally.

There are some Xs unaccounted for however, and that's odds of winning the match if you tie: Wings against Wings, for example.

Let's say I play Hoof with some probability H, Double Horn with probability Dh, and Wings with probability W. No matter what the opponent throws out, playing according to this strategy should deliver you your optimal 1-0 win strategy of X. So, for example, if your opponent goes with Hoof, we get an equation like this:

(H)(X)+(Dh)(0.5)+(W)(1)=X

If they throw Hoof: assuming you put out Hoof too, you win with probability X; in those times you throw Double Horn, you win with probability 0.5; and Wings gives you a sure win with probability 1. The same holds true for the other three things the opponent can throw at you, which gives us a system of equations:

(H)(1)+(Dh)(X)+(W)(0.5)=X
(H)(1)+(Dh)(1)+(W)(0)=X
(H)(0.5)+(Dh)(1)+(W)(X)=X

A similar equation can therefore be derived from this, where you're playing Hoof with probability H2, Double Horn with probability Dh2, Horn with probability h2, and Wings with probability W2. So if you play Hoof, for example, I know that:

(H2)(X)+(Dh2)(1)+(h2)(1)+(W2)(0.5)=X

The solution to this big system of equations gives X≈0.73. It also gives that you should play Hoof, Double Horn and Wings with probabilities 0.40, 0.33 and 0.27, respectively. The opponent should play Hoof, Double Horn, Horn and Wings with probabilities 0.55, 0, 0.21 and 0.25, respectively.

Plays for when the score is 0-0 can be calculated similarly. i'll spare you the maths, but both of you should play Hoof 52% of the time, compared to Double Horn (0%), Horn (24%) and Wings (24%).

Game's stacked in favour of Hoof, huh?