Author's Note
As was the case with my last "Logic Puzzle Adventure", this fic doubles as a puzzle to the reader. Details on how the puzzle works can be found in the next chapter, but anyone who has played the boardgame "Alchemists" should be familiar with the inner workings of how this puzzle goes. For more information about the game that I based this fic on, click here.
Six Potions
Applejack warmly greets her sister’s fellow CMC friends: “You two got here just in time; I’m about to meet most of the others on the field for a buckball scrimmage. She’s in the barn, workin’ on somethin’; lemme let you in.”
She then opens the barn door and indicates a far corner of the interior. Scootaloo and Sweetie Belle observe Apple Bloom hunched over a mini cauldron, a test tube in her mouth and safety goggles over her eyes, as she pours the contents of the tube into the pot. Smoke rises from the bubbling liquid within.
“Apple Bloom!” Scootaloo’s sudden greeting causes Apple Bloom to whip her head around; the test tube flies from her mouth and bounces along the floor. She breathes a sigh of relief upon noticing that the tube did not shatter upon impact.
“Uhps … sorry there.”
“No, it’s all right,” Apple Bloom reassures her friend as she douses the cauldron fire with water. “You just startled me a bit, is all.”
The others walk up to the cauldron to inspect its contents. “So this is what you’ve been working on all morning?” Sweetie Belle inquires.
“What’s all this for, anyway?” Scootaloo adds.
Apple Bloom tests the cauldron’s heat, noting that it’s no longer burning to the touch, she tips over the pot, pours its contents into a beaker, and stops the beaker with a piece of cork. She then places the beaker into a rack that already holds five other concoctions. Satisfied with her progress, she takes off the safety goggles and turns to her friends.
“Sorry, I haven’t been trying to avoid everypony all morning … but I’m trying to figure out how all these ingredients Zecora gave me interact with each other.” Seeing Scootaloo and Sweetie Belle turn to each other in confusion, Apple Bloom continues her explanation.
“Zecora’s been followin’ my progress with potions while workin’ with Twilight. She asked me to come to her home yesterday afternoon, and—“
“Hold on! You went into the Everfree Forest alone?”
“You’re soundin’ like my sister, Scoots!” Apple Bloom replies somewhat icily. “Anyway, I got back before dark.”
“So what does Zecora want with you?” Sweetie Belle asks.
Apple Bloom points to a blanket on the ground nearby. The others take note of a myriad of objects: purple mushrooms, fern seedlings, phoenix feathers, raven feathers, a vial of golden liquid, several blue flower petals, mandrake roots, some dried-out balls of clay.
“This just raises more questions,” Sweetie Belle admits.
“Zecora received a shipment of potion ingredients from her home village about a month ago,” Apple Bloom explains. “She said that each of these particular ingredients holds special properties related to vitality, speed, and wisdom, and that combining pairs of these ingredients could make all kinds of potions … but she admitted that she didn’t know what ingredients had what properties. Then she told me that she hadn’t had time to experiment with any of the ingredients, and asked if I could figure out how everything works.”
Scootaloo ponders Apple Bloom’s words for a moment. “She told you all of that … in rhyme?”
“What can I say?” Apple Bloom responds, brushing off the question. “Zecora has a way with words.”
Shrugging off her friend’s answer, Scootaloo inspects the various potion ingredients on the blanket. “I think I see what most of these items are, but what’s that golden liquid? And what’s with the balls of clay?”
“The liquid is scorpion venom; Zecora assures me that it this particular species of scorpion’s venom may have beneficial powers. And the balls of clay are actually dried-out … uh … toad stool.”
“You mean like the purple mushrooms?”
“Not ‘toadstool’, Scootaloo. Just ‘toad stool’ … like, ‘toad number two’.”
Sweetie Belle recoils slightly in disgust. “Ewww, keep that away from me.” Taking a moment to collect herself, she then continues: “So, how do you know what potion will do what?”
“Weeeeell, that’s the thing, Sweetie Belle … I kinda need your help in the matter? Both of you, actually.”
Apple Bloom’s friends turn to each other, then back to her. Sweetie Belle asks on behalf of herself and Scootaloo, “You want us to drink your potions?”
“Zecora insists that any effects would be temporary; thirty minutes at most. Come on, I could really use your help.”
Scootaloo takes little time to respond: “You know what? Cutie Mark Crusaders are always there for each other! I’m in!”
Sweetie Belle’s enthusiasm is less than that of her pegasus friend, but … “Yeah, I’m here for you too. So what kind of potions can you make?”
“Well, take this potion,” Apple Bloom states as she grabs one of the beakers from the rack. “To make it, I combined the two feathers I had on hand, phoenix and raven. If I had to guess, this should be a potion of speed.”
Scootaloo muses over the thought. “Well I’m already pretty quick. You think that would give me Rainbow Dash speed?” Another thought brightens her outlook: “You think that could let me fly?”
“Gee, I don’t wanna get your hopes up or anything … but if you wanna go first …”
Apple Bloom uncorks the beaker and hands it to Scootaloo, who takes a deep breath before gulping down the contents.”
“So?” Sweetie Belle asks. “How do you feel?”
“All right, I guess. Maybe it takes a few minutes to …” Scootaloo lets out a prolonged yawn. “Sorry, don’t know where that came from … say, is it getting late? …” She then falls to the floor.
“SCOOTALOO!!!” Sweetie Belle rushes over to her friend … and hears heavy breathing. She then turns to Apple Bloom: “You mentioned ‘vitality’ as an attribute, right?”
“Uh, yeah?”
“Well whatever was in that potion, it looks like it leads to anti-vitality; you created a sleeping potion. Say, maybe you could brew up another one of those later; my sister’s been having trouble getting a good night’s sleep in, what with the upcoming Sapphire Shores tour and the work she’s been putting in for the new costume ensembles.”
Apple Bloom mulls over the effects of the first potion. “Huh. So phoenix feather plus raven feather equals anti-vitality. Lemme jot that down.”
Sweetie Belle turns to her sleeping filly friend. “She looks comfortable. I suppose if that’s the worst that could happen … so what other combinations have you tried?”
Having written down the effects of her first potion, Apple Bloom reaches over and grabs another beaker from the rack. “I made this potion using a fern seedling and a blue flower petal. Actually, I thought this would’ve been anti-vitality. Well, maybe it still is.”
Sweetie Belle levitates the beaker from Apple Bloom’s grip and uncorks it. “For science, I guess.” Like her friend before, Sweetie Belle takes a breath and proceeds to down its contents. She waits for drowsiness to kick in, but remains alert.
“Guess I’m oh-for-two, then,” Apple Bloom admits. “So you feelin’ anything.”
“No … and that’s kind of the problem.”
“What d’ya mean?”
“Apple Bloom, I can’t move!”
Sweetie Belle’s lament worries her friend. “Uh oh … are you in pain. Please tell me you’re not in pain!”
“Well … no, not really,” her friend calmly reassures, her head the only feature able to move. “It just feels really weird to be standing here, all numb and such.”
“Strange.” Apple Bloom walks around her unicorn friend and inspects her more closely. She is awestruck by the still nature of her friend. “And remarkable! I guess fern and petal combine to create anti-speed. A paralysis potion.” A grin forms on her face: “I know some ponies I’d like to use this on.”
“Uh, you’re sure this potion is temporary, right?”
“I’m positive … but I guess I shouldn’t wait for those effects to wear off before tryin’ more.” Apple Bloom packs up the remaining vials into her saddlebag and turns to the barn entrance. “I’ll be back soon. Don’t go anywhere.”
Sweetie Belle glares angrily at Apple Bloom. “Seriously?”
“Oh … yeah, right. Sorry ‘bout that again. I should be back in about an hour. If anypony asks, just say I dared you to stand in place for as long as possible.”
Sweetie Belle mutters to herself as Apple Bloom runs off.
A red ball bounces harmless away from the playing field. “Come on, Twilight, that’s the third one you’ve missed today!”
“Sorry, it is my first time playing this,” Twilight shouts out to Rainbow Dash as she trots over to the ball and levitates it into her basket.
“You read the book on buckball, you should be a natural by now.”
“It doesn’t quite work that way, you know.”
“Says the pony who read a book on marathons and finished 5th in her first try,” Applejack wryly counters with a smile.
“Well that’s different. All I have to do there is run, but a unicorn’s duty in this game requires a lot of rapid hoof-eye concentration. Anyway, you couldn’t find another unicorn in Ponyville to assist?”
Applejack fields Twilight’s question: “Well, Rarity’s busy putting together a new ensemble for Sapphire Shores’ upcoming tour. And trust us, we’ve had every other unicorn in Ponyville try workin’ the basket.”
“And besides,” Rainbow Dash adds, “you could use a little less book-reading and a little more sport in your life.”
“Anyway, Appleoosa wants a rematch so Pinkie Pie, Fluttershy, and Snails need all the scrimmage we can give ‘em … and it just ain’t the same usin’ a stationary basket.”
“And don’t forget,” Pinkie adds, “it’s SUPER-AWESOME-FUN!!!”
“OK, you’ve all convinced me about the merits of buckball, but I really need to go, I got some important business to …” Twilight and the others suddenly notice another in their midst. “Oh, hey there Apple Bloom. When did you get here?”
“Oh, I ain’t been waitin’ too long, Twilight. I was just wonderin’ if I could borrow Snails for a minute.”
Snails approaches his classmate and speaks in his usual, stilted tone. “Uhhh, sure. What can I do for you?”
Apple Bloom takes off her saddle bag and pulls out the rack of beakers, selecting one for her unicorn classmate. “Scootaloo and Sweetie Belle have been helping me with a project I’m workin’ on for Zecora. I was hopin’ you could assist me, too.”
Snails pauses for a moment. “Ehhh, what do you need me to do?”
“Just drink this. Don’t worry, it’s safe.” Safe enough, at least. I hope.
Snails uncorks the beaker and sniffs at the contents as the others come in for a closer look. “Sooo, what’s in this?”
“Oh, just a couple ingredients. Little of this, little of that.” Apple Bloom is careful not to inform Snails that she gave him a mushroom and toad stool concoction.
“Wellll, I could use some water. This is close to water. Sure thing!” With that, Snails downs the contents. A minute passes.
“So? Feel anything?”
“Uh, not really,” the unicorn replies. “What’s supposed to happen.”
Apple Bloom’s eyes seek out corners. “Oh, nothin’. Just curious, I guess.”
“So Twilight,” Rainbow Dash asks as she loses interest in the conversation between the foals, “why do you have to leave so soon anyway? We could really use more game time.”
“After the last bout of pony pox that infected the town, I’m trying to create a mathematical model to plan for possible future outbreaks. Such a model could prove very useful for preparation and timely treatment, but the data I’ve gathered doesn’t seem to match with a linear or even a quadratic rate.”
“Uh, have you considered using a logistic model?” Snails’ suggestion causes Twilight to suddenly turn to him.
“What did you say?”
“A logistic mathematical model would seem to be the best way to represent an infectious outbreak. Buuut, I suppose a trigonometric model could work as well, if you think that the number of clinical diagnoses over a year has consistent peaks and valleys. And then there’s the possibility of a logarithmic growth pattern.”
Twilight beams with delight. “Wow! I never knew you were so well-versed in mathematical functions. Thank you, Snails! I have to go and put these ideas into action; I’ll need Spike to dig up my scientific abacus!” Twilight abruptly spreads her wings and giddily flies off.
“Uhhh, I gotta go too. But this was fun. Thanks again for the water, Apple Bloom.” Snails heads off down a path towards Ponyville.
Finally, I made something positive, Apple Bloom thinks to herself, mentally noting that mushroom and toad stool combine to make a wisdom potion. The others, stunned by the turn of events, then turn to the foal alchemist-in-training.
“Whoa … that was awesome, Apple Bloom!” Rainbow Dash exclaims. “You got any more of that stuff?”
“Well, I do … but I’m not sure what the other concoctions I made do. But if you’d like to help a young scientist out …” Apple Bloom indicates the remaining three beakers in the rack. “If anypony wants to try, though, I would sure appreciate it.”
Fluttershy inspects the three remaining beakers. “Do any of these share an ingredient with the one you gave Snails?”
“Uh sure, this one does.” Apple Bloom indicates one of the beakers, politely hiding the fact that the shared ingredient is toad stool and the other ingredient is phoenix feather.
“Well, I do feel a little more daring now.” Fluttershy chuckles to herself, her buckball skills giving her added self-confidence. “I’ll try that one.” She grabs and uncorks the beaker and swallows the potion.”
“Well?” Rainbow Dash inquires. “Anything?”
“Not really. Oh, I hope I didn’t ruin your experiment, Apple Bloom.”
“Hey, a non-result can give just as much information,” the foal cheerfully replies.
“Yeah, well, nothing more to see here,” Rainbow Dash declares. “Fluttershy, wanna grab something at Sugarcube Corner? Let’s race; loser treats.”
“Oh, you know you’d win that race. You always win.”
“Fine, I’ll give you a head start. You start while I count to 10, then I’ll chase you. Ready?”
“OK.”
“OK, go …”
Before Rainbow Dash can utter “1”, Fluttershy bolts off leaving a pink trail of vapor in her wake. She and the three earth ponies gape at the vapor trail. “Uh … what just happened?”
“I dunno, but I think you owe Fluttershy a treat,” Applejack sniggers as her sister mentally takes note: phoenix feather and toad stool combine to make a speed potion.
“Yeah, well two can play that game!” Rainbow Dash quickly grabs one of the remaining beakers, opens it and downs the potion before Apple Bloom can react. Uh oh; that one contained a blue petal like the one that paralyzed Sweetie Belle … and it also contains scorpion venom. The foal silently observes Rainbow Dash’s reaction.
“All right, now I’ll catch up to her … and when I do … *chuckle* I’m gonna show her …” The blue pegasus suddenly bursts out in laughter.”
“Rainbow Dash, what the hay’s gotten into you?”
Tears flow down Dash’s face as she responds, her words interrupted by consistent guffawing: “I *snicker* … I just thought about how *haha* … how silly she’s gonna feel when *heehee* … when she *chuckle* … when she learns that …”
“YEAH????” Pinkie urges.
“When she *giggle* … when she learns that I’m not there to pay for her treat! BAHAHAHAHAAAA!!!”
Rainbow Dash falls to the ground, overcome with hysterics. Pinkie Pie also falls to the ground laughing, sharing in a joke that she honestly doesn’t get, but not caring as her friend is having so much fun thinking about the idea. Apple Bloom mentally observes that the blue petal / scorpion venom concoction resulted in an anti-wisdom potion. Applejack, unfazed by the bout of hysterics playing out before her, turns to her little sister and glares at her.
“Well I think you’ve caused enough damage for one day, missy. Let’s go.”
“Wait, I still got one more beaker. I don’t suppose you’d want to—“
“OOO, OOO, MY TURN!!!” Without warning, Pinkie Pie jumps up, rushes over, grabs the beaker, opens it and polishes off its contents.”
“Pinkie Pie,” Applejack scolds, “have you lost your mind???”
Scary thoughts rush through Apple Bloom’s head: Pinkie Pie’s crazy enough as is; what’ll happen if she gets more insane? Or what if she gets super-fast like Fluttershy? Or if that potion adds vitality; she’s already as buzzed as a hummingbird. What did I put in that one? Oh yeah, mushroom and mandrake. Oh Celestia, what have I done???
Apple Bloom shuts her eyes tightly, not wanting to know what reaction Pinkie would have to the potion … but nothing happens. Carefully, she opens her eyes again, to see Pinkie grinning wildly and staring right back at her.
“That was a really tasty potion you made there. Reminds me of the soup I used to have when I was a filly on the rock farm.”
“Wait, so you don’t feel any different? You’re not sleepy, or speedy, or … more Pinkie-ish?”
“Nope! Same-old fun-loving Pinkie Pie, at your service … but right now, probably better in Rainbow Dash’s service. I’ll help her to town as she finishes laughing at that joke that wasn’t really funny.”
Pinkie bounds over to Rainbow Dash and helps the pegasus to her feet; the latter continues to laugh wildly at nothing in particular; Pinkie laughs with her as the two walk away.
“OK, that’s it!” Applejack scolds. “No more potion-testin’ for you!”
“But … but I’ve only made 6 potions! What am I supposed to tell Zecora?”
“You and I are gonna walk over to her place first thing tomorrow mornin’. We’re gonna give back any ingredients you got left from her, and then you’re gonna be doin’ extra chores for the next week. Got it???”
Apple Bloom nods in begrudging acceptance, knowing full well what that tone of voice meant.
Climbing the steps of the CMC clubhouse and entering, Apple Bloom is surprised and relieved to find her two previously incapacitated friends jotting notes down on a sheet of poster paper. “What’re you two doin’ here?”
“We only got here a couple minutes ago,” Scootaloo explains. “That was when that paralysis potion wore off. Sweetie Belle told me all about it while she was stuck in place.”
“Yeah, sorry again for puttin’ you two through that, just to make myself look good to Zecora,” Apple Bloom sadly admits.
“Hey, you don’t have to apologize to me. Best sleep I’ve had in a long time.”
“It wasn’t so bad for me either,” Sweetie Belle adds. “Didn’t hurt or anything, just a strange sensation. Though I did have to tell Granny Smith that you dared me to strike a pose for a half-hour. By the way, you’re treating me the next time we go to Sugarcube Corner. You know, to deflect suspicion,” she concludes with a grin.
“Well thank you both again for all your help … but my potion-makin’ days are over, at least usin’ those ingredients. Applejack’s takin’ me back to Zecora tomorrow morning to return all the unused components.” Apple Bloom then scans the poster. “Hey, are those my notes?”
“Yeah, you got us all curious about this,” Scootaloo states, “but we couldn’t make manes or tails about most of it. Maybe you can explain what you were actually trying to accomplish.”
Apple Bloom’s outlook brightens immediately: “Sure, I’d love to!” She excitedly runs over to a cabinet and opens a drawer, pulling out a glove with a marker attached to it. She puts the glove on and walks over to the whiteboard.
“Where’d you get that,” Sweetie Belle asks.
“Applejack made it for me. She got the idea from some pony in Manehattan. Nice, isn’t it! Now I can draw on the board and still talk to you without havin’ the marker in my mouth. I got a couple more in there if either of you want.”
Sweetie Belle declines, using her magic to move the free-standing marker around, but Scootaloo accepts and dons another marker-embedded glove. Apple Bloom then puts up a fresh sheet of poster paper and proceeds to write the letters “V” “S” “W” at the top of the paper, followed by eight groups of three-letter strings: “PPP” “PPN” “PNP” “PNN” “NPP” “NPN” “NNP” “NNN”.
“We got eight ingredients here,” Apple Bloom commences, “and each one has a unique combination of special properties related to vitality, speed, and wisdom. For each property, an ingredient will either give off a positive or a negative reaction when properly combined with another ingredient. So for example: one ingredient is classified as PNP: that means that a potion created with it will either be a vitality potion or an anti-speed potion or a wisdom potion.”
“So when I was paralyzed, that was—“
“An anti-speed potion, Sweetie Belle. The two ingredients I used in your potion must’ve both had an N in the middle. And the same thing with Scootaloo: the two ingredients I used in your potion must’ve had an N in front.”
“OK, so let me try something,” Scootaloo declares. She writes the strings NPP and PPN on an empty corner of the paper. “I just want to make sure I understand this. So if we combine these two ingredients, we’ll get a speed potion?”
“You got it,” Apple Bloom cheerfully acknowledges. “Because both ingredients have a P for the speed aspect. And what if you have NNP and PPP?”
“You’d get a wisdom potion,” Sweetie Belle answers, “because both of those ingredients have a P for the wisdom aspect. OK, that doesn’t seem so hard.”
A thought pops into Scootaloo’s head: “Wait a minute: what if the two ingredients share two characteristics. Like, what would NPP and NPN combine to give you?”
“Yeah, those are tricky,” Apple Bloom admits, “but Zecora told me how those all balance out. What were her exact words? … Oh yeah: ‘Wisdom over speed, it’s true … but speed tops vitality, too … and vitality over wisdom, who knew?’ ”
Sweetie Belle and Scootaloo look to each quizzically, then turn to Apple Bloom. “What does that mean?”
“It confused me at first too, Scootaloo, but it basically means that if two aspects are the same, then one specific aspect always takes precedence … and it’s all balanced between the three. Just like if you had a rock, a pair of scissors, and a piece of paper: the rock could crush scissors, the scissors could cut paper, and the paper could cover the rock.”
“But couldn’t the rock be placed on top of the paper?”
“And what if you had other objects, like a lizard, or—“
“The point I’m tryin’ to make is, the three properties balance each other out. Look, I’ll show you:”
Apple Bloom writes NPP and NPN on another empty corner of the paper, then circles the first letter (N) and middle letter (P) in each triple. “Since these two ingredients have the same property for both vitality and speed, they’ll combine to form a speed potion. That’s the point of that rhyme; it’s how you know you won’t make an anti-vitality potion instead. Here, I’ll show you another example.” She then writes NNP and NPP on the paper, and has the others mull over the possibilities.
“So,” Sweetie Belle begins apprehensively, “both of these ingredients are anti-vitality and pro-wisdom … and since it’s vitality over wisdom, that means these two ingredients would form an anti-vitality potion.”
“You got it!” Apple Bloom happily declares. “And here’s something I figured out: any ingredient can be combined with each of the other seven, and every property will take precedence exactly twice among those seven.”
“Whoa whoa whoa, you completely lost me there,” Scootaloo admits.
“Here, let me demonstrate.” Apple Bloom pulls out another sheet of poster paper and writes NPP at the top. She then lists all seven remaining triples underneath: PPP, PPN, PNP, PNN, NPN, NNP, NNN. “I claim that two of these seven will combine with NPP to make anti-vitality, two will combine with NPP to make speed, and two will combine with NPP to make wisdom. Can you figure out which ones work with what?”
Scootaloo and Sweetie Belle examine the strings, mentally trying to figure out how each combines with NPP. “Well three of these are easy,” Scootaloo finally states. “NNN must make anti-vitality since the only property they have in common is the first letter. And PPN must make speed for the same reason, but with the middle letter. And PNP must make wisdom since they have the same last letter.”
“Very good,” Apple Bloom states. “Now which other ingredient would combine with NPP to make anti-vitality?”
“OH,” Sweetie Belle exclaims, “it’ll be the NNP one! Because they share the same property for both vitality and wisdom, and vitality beats wisdom!”
“I see,” Scootaloo adds, “and NPN would combine with it to make speed. And PPP would combine with it to make wisdom!”
“That’s perfect!” Apple Bloom writes their notes under each triple: either NNN or NNP would combine with NPP to make anti-vitality, either PPN or NPN would combine with NPP to make speed, and either PNP or PPP would combine with NPP to make wisdom.
“So what about that last one,” Sweetie Belle asks, indicating the PNN triple.
“Yeah, each ingredient has a polar opposite with no attributes in common: when those two are combined, you get a potion that does nothing. Zecora referred to such a potion as ‘soup’.”
“Wow,” Scootaloo admits, “you really know how all these ingredients react to each other. Just one thing … which of these ingredients is the NPP one?”
“Well, that was the whole point of my testing,” Apple Bloom states dejectedly. “I thought that by trying all possible combinations, I would know exactly which ingredient went with each triple … but I was only able to test out six potions, including the ones you two drank.”
Sweetie Belle ponders for a moments. “But surely you got some information from those tests, right?”
“Yeah, I got six results in all.” Apple Bloom then writes down her findings:
Phoenix Feather + Raven Feather = anti-vitality
Fern + Blue Petal = anti-speed
Mushroom + Toad Stool = wisdom
Phoenix Feather + Toad Stool = speed
Blue Petal + Scorpion Venom = anti-wisdom
Mushroom + Mandrake = soup
Sweetie Belle looks over the list. “Well, phoenix feather helps make anti-vitality, so its first letter is definitely N.”
“And it also helps make speed,” Scootaloo adds, “so its second letter is definitely P.”
“Great, so phoenix feather is either NPN or NPP,” Apple Bloom concludes. “But I never used it with anything else.”
“We still got other results here; let’s see how much more we can figure out.” With Sweetie Belle’s urging, the three proceed to go through their list of six results and make further deductions …
Applejack and Apple Bloom eye Zecora’s tree house in the near-distance. “Almost there,” Applejack states. “Sorry again that you have to end this experiment early, but we really can’t risk any more unforeseen consequences. I gotta say, though, you seem happier than I thought you’d be.”
“My friends helped out,” her sister cryptically replies. Applejack brushes off the comment and strolls up to the front door, giving it a rap with her forehoof. Zecora answers the knock.
“I was not expecting you today; is there something you have to say?”
“Sorry to bother you so early, Zecora, but Apple Bloom is here to return all the remaining potion ingredients to you … and she has something else she has to say.”
Applejack nudges her sister over to Zecora, expecting to hear the words ‘I’m sorry’. Instead …
“Zecora, I cracked the code.”
Author's Note
At this point, you the reader now have enough information to determine which label (from PPP through NNN) goes with each ingredient. If you wish to PM me the solution, I can verify for you; otherwise, feel free to wait for the final chapter that will detail said solution. If you wish to post your solution here, I only ask that you do so with hidden text, so others will not accidentally read the solution before figuring it out themselves.
Apple Bloom Explains It All
“Apple Bloom!” Applejack angrily stares down her little sister as she continues. “I done told ya not to make any more of them crazy potions!”
“I didn’t, sis! I swear I didn’t.”
“Really? So you’re gonna tell me that you figured out how all them weird ingredients interact with each other, just on the basis of six tests?”
“Not all by myself; Scootaloo and Sweetie Belle helped out a lot. We figured everything out last night. I can tell you everything you need to know about those eight ingredients, and I can prove it. And if I’m wrong, I’ll do double the chores you gave me for punishment.”
Applejack mulls over her sister’s assertion. “All right … go ahead and explain yourself to me and Zecora.”
“I must admit I’m most intrigued. By all means, Apple Bloom, proceed.”
Apple Bloom takes off her saddlebag and pulls out several pages of notes in additional to the unused potion ingredients. “This first page of notes details the results of the six potions I created,” she explains as she hands a paper to Zecora.
Phoenix Feather + Raven Feather = anti-vitality
Fern + Blue Petal = anti-speed
Mushroom + Toad Stool = wisdom
Phoenix Feather + Toad Stool = speed
Blue Petal + Scorpion Venom = anti-wisdom
Mushroom + Mandrake = soup
“Now,” she continues, “the eight ingredients match up in some way to the eight possible combinations of vitality, speed, and wisdom. I refer to these using three-letter labels, where the letters are all either P for positive or N for negative, and where the first, middle, and last letters refer to vitality, speed, and wisdom, in that order. The eight labels are PPP, PPN, PNP, PNN, NPP, NPN, NNP, and NNN.”
Apple Bloom then pulls out another page of notes. “Now two of the six potions use phoenix feather, and those two potions were anti-vitality and speed; that means that phoenix feather is either NPP or NPN. Similarly, two of the six potions use toad stool, and those two potions were wisdom and speed; that forces toad stool to be either PPP or NPP. More specifically, phoenix feather and toad stool combine to make a speed potion. Now if phoenix feather were NPP, that would force toad stool to be PPP … but in that case, they would combine to make a wisdom potion, not a speed potion. That means that phoenix feather’s got to be NPN.”
Zecora smiles. “So far you’re reasoning sounds okay. What else do you have to say?”
Apple Bloom continues reading from her page. “Now consider raven feather. Since it combines with phoenix feather to make anti-vitality, it has to be either NPP, NNP, or NNN … but it can’t be NPP, since that would combine with phoenix feather to make a speed potion, not an anti-vitality potion. So it has to be either NNP or NNN. The thing is, it can’t be NNN either.”
“Now hold on,” Applejack interrupts. “I know I don’t get everything you’re rattlin’ on about, but how can you possibly know that this ‘raven feather’ can’t be that all-Ns label?”
“Because phoenix feather has the anti-wisdom attribute, and so does both the blue petal and the scorpion venom, since they combine to create an anti-wisdom potion. And there’s only four ingredients with the anti-wisdom attribute; the fourth one has to be mandrake, since its attributes completely cancel out when combined with mushroom, and mushroom has a positive attribute in wisdom as shown by the potion made when combined with toad stool. That’s why raven feather can’t be NNN, so it’s got to be NNP.”
Apple Bloom’s explanation was enough for Applejack to bite her tongue for the remainder of her sister’s presentation.
“Now the fern seedling also has to have the wisdom attribute, for the same reason as that for the raven feather. And because it combined with the blue petal to create an anti-speed potion, it must be either PNP or NNP … but NNP is already taken by raven feather, so fern seedling must be PNP.”
“So far I am most impressed,” Zecora accedes, “but now how do you deduce the rest?”
“Well, the three remaining labels that end with N are PPN, PNN, and NNN; these have to be blue petal, mandrake, and scorpion venom, in some order. But blue petal can’t be PPN since it combines with fern to make an anti-speed potion, and mandrake can’t be PPN since it’s the opposite of mushroom, and mushroom can’t be NNP since we already know raven feather is. That means scorpion venom must be PPN. And now, I know that blue petal has to be NNN; if it were PNN, it would combine with scorpion venom to make a vitality potion, not an anti-wisdom potion. That leaves mandrake to be PNN … and since mushroom is the opposite of mandrake, it has to be NPP. And that leaves only the toad stool, which must be PPP. And … and that’s it, I guess.”
Apple Bloom’s voice trails off, having completed her argument. A broad smile forms on Zecora’s face.
“Bravo, Apple Bloom, you’ve passed the test! Surely, your deduction skills are the best!”
“Well, I couldn’t have done all this without my friends.”
“All the same, you’ve done very well. You have a real gift, I can tell.
Applejack quietly utters ‘We’ll I’ll be,’ then simply smiles at the spectacle.
“I must now put this information to good use, as delaying no longer has an excuse. I thank you again one last time, your abilities are most prime.”
Apple Bloom nods in acceptance and turns to the door, with Applejack following as they depart.
“Apple Bloom,” her sister starts as they walk through the forest towards the farm, “I gotta say, I’m mighty impressed by you an’ your friends. I don’t think any Apple has ever demonstrated such ability in potions or logical reasonin’ before. You got your whole life in front of you, an’ you’re already well on your way.”
“Thanks, Applejack.” Apple Bloom beams, very touched by her sister’s comments.
“Of course, you still got your extra chores for the week.”
“WHAT???” Apple Bloom’s head spins angrily towards her sister. “We had a deal???”
“Yes we did: you agreed to do double the chores if you were wrong, and as it turned out, you were right … but I never agreed to rescind those chores if you were right. You didn’t make no mention of ‘double or nothing’.”
Apple Bloom mutters an incomprehensible ‘ponyfeathers’. Her sister chuckles, then embraces her: “You still got a lot o’ learnin’ left to do … but all the same, I’m real proud of you.”
