Fox-Chicken-Grain Puzzle

"I've got one word for you: Trebuchet!"

RATS! Your goose is cooked!

— One failure message for this puzzle in Blob Manager Demo for the Apple Macintosh

A Stock Puzzle, subset of the Inventory Management Puzzle. You are a farmer taking a fox (or a wolf), a chicken (or a goose), and a sack of grain to market (don't ask why you're taking a fox and/or wolf to market) and you come across a river. The only way across the river is by a small boat, which can only hold at most you and one of the three items. Left unsupervised, the chicken will eat the grain or the fox will eat the chicken (however, the fox won't try to eat the grain, nor will the fox or the chicken wander off). What's the quickest way to get everything across the river?

The standard answer is:

1. Take the chicken across
2. Come back with the boat empty besides yourself
3. Take the grain (or the fox) across
4. Take the chicken back
5. Take the fox (or the grain) across
6. Come back with the boat empty besides yourself
7. Take the chicken across

This puzzle's primary difficulty to those new to the puzzle is in realizing that one must consider the possibility of taking an action that seems detrimental or a step back from their original goal in order to ultimately complete it.

May also appear with different animals and vegetables, such as wolves, sheep, and cabbages. (The version best known in the former Soviet Union, for example, has a wolf, a goat, and cabbage.) A "jealous husbands" (also known as cannibals and missionaries, or knights and squires) variant has three couples trying to cross a river with a two-person rowboat, but none of the men will allow his wife to be alone with either of the other men on either side of the river (or, cannibals cannot outnumber missionaries, lest the latter attacked and eaten; or each knight's squire is too afraid to stay with the other knights). This one can be solved in eleven steps.

This is an ancient puzzle. The oldest known example was found in Propositiones ad Acuendos Juvenes, which dates to the late ninth century.

A more complicated version, but which operates on much the same principle, involves a barrier (usually a bridge), four people who all move at different rates, and some item that is required in order to cross the barrier (most often a flashlight). The puzzle is to get all the people across within a specified amount of time, which seems to be too short. Probably the most well-known version of this is:

Four men want to cross a bridge. They all begin on the same side. It is night, and they have only one flashlight with them. At most two men can cross the bridge at a time, and any party who crosses, either one or two people, must have the flashlight with them.
The flashlight must be walked back and forth: it cannot be thrown, etc. Each man walks at a different speed. A pair must walk together at the speed of the slower man. Man 1 needs 1 minute to cross the bridge, man 2 needs 2 minutes, man 3 needs 5 minutes, and man 4 needs 10 minutes. For example, if man 1 and man 3 walk across together, they need 5 minutes.

How can all four men cross the bridge within 17 minutes?^{The Answer}Men 1 and 2 cross, 1 (or 2) returns, 3 and 4 cross, 2 (or 1) returns, 1 and 2 cross.

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Examples:

Alternate Reality Games

• Perplex City: The first puzzle appears, with a professor, a senior fellow, and a cocktail. The second shows up nearly verbatim.

Anime & Manga

• Dr. STONE references this puzzle (with corn in place of the grain) when the protagonists find themselves in a similar situation of having to move everyone in their group across a rope line with a strict weight limit, while not allowing the villain they're holding prisoner to be alone with anyone he could escape from or talk into betraying the team.
• The cannibals and missionaries version is mentioned in Umineko: When They Cry, with wolves and sheep.

Comic Books

• In the Puzzle Planet from Skrulls vs. Power Pack, the kids find a room with three alien critters with two who only want to eat one of the other critters and a pipe leading to another room that's only big enough to take one of the critters at a time. Katie figures out the back-and-forth method, opening the door to the next room after getting them all through the pipe.

Comic Strips

• Parodied in a Dilbert strip featuring the question asked to an immoral job interviewee, whose proposed solution is to take out insurance on the chicken, eat it, then blame the fox.
• Pearls Before Swine also parodies this one, with Rat giving the riddle in standard form to Pig. Pig's answer is "Buy a bigger boat."

Gamebooks

• The knights and squires version turns up in the The Crystal Maze gamebook.
• The puzzle appears in J.H. Brennan's (better known as author of the GrailQuest books) Dracula's Castle, where you have to travel with a cat, a dog, and a mouse in a lift. However, the twist is that the cat can't bear to take the lift more than twice, meaning the puzzle is impossible and the correct "answer" is to get confused and give up.
• This puzzle is featured quite humorously in a Czech-language gamebook Norik: You need to cross a river and you meet a farmer with a boat, a wolf, a goat, and a basket of cabbage and need to help him get the three "items" to the other side of the river. When he returns back to get the goat, you must convince him to get you over the water first. Then, when he returns to finally get the goat, the wolf grows tired of not being able to eat the goat and eats the cabbage instead. Norik (your alter-ego) shouts at it and the wolf runs off, which also results in the rest of the cabbage being thrown into the river. As you hear the farmer shout profanities at you, you decide to not wait for him and go on. Later, you arrive at a farmhouse, where you could sleep, but decide not to after it turns out to be the farmer's house, when he runs after you, pulling (and strangling) the goat after him.

Fan Works

• The Arithmancer: Like in canon, the door-knocker on the entrance to the Ravenclaw common room gives puzzles in lieu of a password, of which this is one in the fic. Ginny suggests Cutting the Knot by casting Freezing Charms on the animals and conjuring a bigger boat, which the door deems an "acceptable alternative".

Literature

• Ian Stewart's popular-mathematics book The Magical Maze opens with this, as an example of a maths problem most people are familiar with. To make it a bit more interesting he frames it as the Panther-Pig-Porridge puzzle.
• Near the end of John Varley's Red Thunder, Manny mentally compares the situation of saving several trapped people from the wreckage of a spaceship to this puzzle. As he arranges to get them out, he solves it in his head.
• This is one of the puzzles used during the Engagement Challenge in The Sleeping Beauty.
• The Piers Anthony novel With a Tangled Skein has this near the ending, with the Missionaries/cannibals variant. The complication is that there are three women and three demons, and if the demons outnumber the women at any point, the women will be raped.

Live-Action TV

• Subverted in Beauty and the Geek. The puzzle included a rowboat, a sack of grain and a toy chicken and fox. The solution was to take them all at once since toy animals don't eat each other.
• This forms the basis of the primary plot for the Between the Lions episode "Farmer Ken's Puzzle", where Lionel attempts to solve the puzzle, here depicted as a computer game (though a cat replaces the fox). The pigeons try to give him advice, which causes him to fail the first two times, and after they give up and leave it alone for a while, his little sister, who they've been constantly brushing off as "too young" for the game, solves it.
• One episode of Camp Cariboo has Tom pull this on Mark, using a fox, a goose, and a sack of corn.
• Death in Paradise: DI Goodman likens how the Mystery of the Week of "Death of a Detective" was carried out to this puzzle. Fidel keeps trying to figure out the puzzle for the rest of the episode.
• Fargo
  • In the "A Fox, a Rabbit, and a Cabbage" episode, Budge asks Pepper this riddle to pass the time while they are assigned to the file room. Pepper gets hung up on the details and eventually provides a unique answer.
    Pepper: A Turducken.
    Budge: A what's that now?
    Pepper: He stuffs the cabbage in the rabbit and the rabbit in the fox, and he eats all of them.
    Budge: That's not the answer.
    Pepper: It's an answer.
  • In the subsequent "Morton's Fork" episode, Budge asks Lester the riddle while driving him back to his home and he gets the correct answer right away.
• Mongrels references this in the first episode with Nelson the fox, his chicken "girlfriend" and a bag of grain they were eating. They solved it by knocking out the boat's owner and stealing it.
• Parodied in Mystery Science Theater 3000, in the episode "Killer Fish". During the movie, most of the movie's characters end up on a slowly sinking boat in a piranha-infested river with a crudely built two-person raft to save them. During a subsequent host segment, the crew of the SOL liken their predicament to one, with details like the hero and the villain getting into another fistfight if they're taken over together. Their eventual solution is that the people on the boat should make themselves into a raft, except for campy photographer Ollie, who everyone knows isn't making it out of this situation (and indeed, when they go back into the theatre Ollie dies more or less instantly).
• In an episode of The BBC's version of The Office, Gareth and Tim are assigned to solve this puzzle as a problem-solving exercise. As always, Gareth complicates things by taking it literally...
  Gareth: Get his wife to help.
  Tim: He doesn't have a wife.
  Gareth: All farmers have wives.
  Tim: This one doesn't; he's gay.
  Gareth: Well then, he shouldn't be allowed near animals, should he?

Radio

• The puzzle is brought up in the The Infinite Monkey Cage episode 'How to Beat the House and Win at Games' (though here the elements become a traveller with a wolf, a goat, and some cabbages). However, the discussion of the puzzle becomes derailed when the panel starts wondering exactly how this situation came to be (mainly, why the traveller is travelling with a wolf, a goat, and some cabbages). And while the solution is eventually explained it is also pointed out (and confirmed by a Google search) that the wolf would eat the cabbages as well since wolves are opportunistic carnivores.

Video Games

• An Adobe Flash game has a more complex variant involving a raft, eight people and a convoluted set of rules. Good luck!
• A variation of this appears near the end of Broken Sword: The Sleeping Dragon; a murderer, a witness to his crime, and the brother of the murder victim must all cross the river to reach the murder trial. The victim's brother is analogous to the fox, the murderer is analogous to the chicken, and the witness is analogous to the grain.
• Crusader of Centy has this puzzle in the witch's house but with a chicken, a caterpillar, and a flower. The caterpillar then decides to join your party to see the world. And it's a talking flower.
• Part of the cockatrice sidequest in Final Fantasy XII requires bringing the cockatrice Sassan across a river to meet a friend on the other side. Sassan is afraid of Nathyl (a tame wolf), and there's also a village boy named Arryl. The solution is to bring Nathyl to the other side, then bring Arryl over to play with Nathyl and keep him occupied, and finally bring Sassan over.
• The first Midnight Mysteries uses the "jealous husbands" variant, involving two police officers, two sailors, two young boys, the player character, the boatman needed to transport the entire party across a river, and a boat that can carry a maximum number of three people, including the boatman. Aside from the boatman (not the player character, surprisingly) needing to be on the ferry at all times, the other rules are that the sailors must be under the watch of the officers, and the young boys must be accompanied by an adult (you or one of the policemen) at all times during the river crossing.
• Appears as a series of wood-inlay pictures on a puzzle box in Nancy Drew: The Last Train to Blue Moon Canyon. It uses a dog, a cat and a bird, presumably because a bag of grain would be hard to identify in silhouette. Nancy deduces the animals' starting side for you, from no clues whatsoever!
• In Poptropica, you have to solve this puzzle on Nabooti Island. As a reward, you are told about a secret cave behind some grass where you can find a jewel.
• Naturally, various versions of this puzzle pop up in the Professor Layton series.
• In Puzzle Clubhouse, a decorative fountain referencing the fox-chicken-grain puzzle won the popular vote, becoming a permanent part of Puzzle Clubhouse's landscaping.
• Runescape:
  • The game has one of these, completing a similar task for Temple Knight Sir Sisyphus.
  • The bridge type showed up in another quest.
• The obscure dating game Sprung on the Nintendo DS had a variation to this on Brett's story. At one point Brett will be asked to go to Sanctuary with Becky, where he will bring his buds Lucas and Danny while she brings Alex and Erica. The catch, however, is that Becky wants a calmer night, so she doesn't want any funny business (nevermind that Sanctuary is a raving night club where the nameless other people not mentioned in the game are probably doing just that). The puzzle comes where Brett meets everyone but Becky at the front of the club and he has to get all of them inside one by one. However, if Lucas and Alex or Danny and Erica are left alone and Brett comes back to them later, he will catch them making out, leading to Becky to see this, her announcing the night was ruined and you getting slapped with a game over. The puzzle is extended further because it's not only a matter of getting everyone inside, but also a matter of keeping everyone happy which means a lot of shuffling out people whom are already fine inside (such as dragging Danny out because he gets panicked over the sight of too many people, or dragging Lucas out for pep talk). Further rules are also added as time marches on, including how the aforementioned couples can later be left alone without problems after an event happens where Brett talks them down, or how new pairings are made that can't be left alone without you interfering with them (such as how, at one point, Danny and Lucas will fight if left alone).
• Tower Core, the fourth in the Core series of Flash games has five things you need to move from one chamber to another, with the field that suppresses them only active in one chamber at a time: The Zog-Beast will eat the Mog-Rat, the Glaw-Than fly will eat the Zog-Beast, the Muk-Tar plant will eat the Glaw-Than fly, and the cannister of radiation will kill the Muk-Tar plant.
• A variant of this turned up in Uninvited, where if you didn't choose correctly between a small bird, a housecat, and a snake, then one of the remaining animals would eat the third, and then it would slaughter you (the solution was to take the bird, since the snake is too full to move after it's eaten the cat).
• Zork Zero has you collect a fox, a chicken and an earthworm, all to be taken across a swamp and used in "Borphbelly Stew".

Web Animation

• Overly Sarcastic Productions: Red references this puzzle in Journey To the West: Part VII: When Tripitaka and his party need to cross a river and a ferryman offers to take them across but in multiple trips (which turns out to be an attempt to kidnap Tripitaka), Sun Wukong adds, "We also need to bring this chicken, this fox and a bag of assorted grains."

Webcomics

• Breaking Cat News has a strip where the four cats are trying to sleep together on the Man, but Lupin and Goldie can't be next to each other, Elvis can't be next to Lupin, and Puck would prefer not to be next to Elvis. Puck brings up the puzzle, and Goldie and him question why the farmer had a fox after their own situation is sorted.
• Full Frontal Nerdity does it, with the Missionaries and Cannibals variant.
• xkcd:
  • Referenced in "Designated Drivers."
  • A later strip proposed an alternative way to solve this puzzle.
    1. Take the goat across.
    2. Return alone.
    3. Take the cabbage across.
    4. Leave the wolf. Why did you have a wolf?
  • "Boat Puzzle" starts with the classic puzzle, but then more people show up with even more ridiculous requests (one person has two wolves and 100 cabbages, another has a goat that eats the wolf, etc.).
• This webcomic throws a wrench into the classic riddle by allowing the wolf to eat the fruit in this case. It also throws a second curve ball by replacing the chicken with a duck for this riddle, and it turns out that there's nothing that says you can't use the rope depicted in the boat to tow the duck behind the boat. The riddle is then solved in just three moves—take one item across, return, take the other item across, all while towing the duck with the rope, since the duck can float.

Web Original

• Advent of Code includes a more complex version of the "jealous husbands" variant as 2016 day 11. There are four floors with various chips (the "wives") and generators (the "husbands") scattered across them. Any chip that ends up together with any generator while not also on the same floor as its matching generator gets destroyed, failing the puzzle. You can take either 1 or 2 items with you (not zero or more than two), and you can only move one floor at a time. You have to move all items up to the top floor. Part 2 adds two extra chip/generator pairs.
• The Internet comedy duo BriTANicK used this as the starting point for one of their videos, wherein Brian asks Nick a number of brain teasers. Not that Brian cares about the answers; he's just obsessed with stealing Nick's Klondike bar, and the thought of Nick making out with his girlfriend.
• Cleolinda Jones describes The Twilight Saga thus:
  Yeah, it's like, Bella wants to be a vampire but she doesn't want to be a vampire before she's had sex as a human, and Edward doesn't want her to be a vampire but he wants to get married, but Bella doesn't want to get married unless she can be a vampire, but Edward won't have sex with her until they get married, and then you put the fox and the grain in the boat and you leave the goose back on the riverbank.
• Ted uses the four people bridge crossing variant for this riddle video, and the "Cannibals and Missionaries" variant for this riddle video.
• IT specialist site thedailywtf.com references the more complicated version with the bridge and four men here as the way to not do a job interview when looking for an IT specialist. Their preferred answer: leave the slow one behind!

Western Animation

• Happens in Class of 3000.
  • One episode had Sunny put his class through this task as training for an upcoming concert. Tamika lampshades it:
    Tamika: Everybody knows that riddle!
    Sonny: What riddle? (pulls curtain open, revealing a chicken, a coyote, and a sack of corn)
  • Eddie and Philly Phil manage to get through it in fewer than seven steps due to Eddie bribing the coyote with a $100 bill to not eat the chicken.
    Philly Phil: What's a coyote gonna do with a hundred dollars?
    Eddie: If cartoon memory serves me correctly, he'll spend it on Acme Rocket Skates.
• Toonami's Intruder II special event begins with TOM and SARA discussing the puzzle with a fox, a chicken, and a cabbage. They're interrupted by the sensors finding a mysterious ship nearby that opens fire on the Absolution before they can discuss the solution.
• In The Powerpuff Girls (2016) episode "Splitsville", Bubbles has to help a farmer get his goose, fox, and bag of seeds across the river. It starts out normal, then gets ridiculously complicated with the addition of nosy tourists, a Robber Baron, the starting lineup of the Townsville girls' basketball team, Sherlock Holmes, and the Raptor King. And to top it off, at the end the farmer realizes that his farm was on the ''other'' side all along.
  Bubbles: Why do you even need all these things in your farm?
  Farmer: Listen, do you know of a better way to grow radishes?
• Parodied by animated short film "Rubicon" by Gil Alkabetz. As one viewer once commented: That wasn't a cabbage, that was a peyote!
• The Simpsons:
  • Showed up in the 20th season episode "Gone Maggie Gone". Homer is trying to get across a river with Maggie^note chicken, Santa's Little Helper^note fox (who is trying to tear up Maggie's doll), and a jar of candy-coated rat poison^note grain. Then this trope is subverted when Homer brings Maggie first and she just crawls off, setting off the plot for the rest of the episode. While Homer is getting Maggie across the river, Santa's Little Helper just swims his way until Homer berates him for not paying attention to the puzzle.
    Homer: Why did I bring the baby and the dog to the poison store??
  • In the same episode, Cletus asks Homer for help with getting a fox, duck, and corn across, but then "the puzzle done worked itself out" when both the corn and the duck are eaten.
• In Space Ghost Coast to Coast, such a puzzle was used as a means of describing the concept of "branding" (no, NOT like branding with a hot iron). In typical Space Ghost fashion, the puzzle was... less-than-helpful in explaining the concept. Note that no answer was given.
  Space Ghost: Let's say you have a cow, a rowboat, and The Big Man.
  Zorak: You mean, Clarence Clemons?
  Space Ghost: Of course. Now, the cow wants to transport Clarence across the river. But remember, the cow is on fire, and Clarence has no hands or bucket, so he has to utilize his hooks, and the mighty power of his saxophone!
• In Star Trek: Prodigy, Janeway has the "cadets" do this as a training and team-building exercise... on the holodeck, with simulations of a real fox, chicken, and bag of grain. Zero gets on the right track by realizing that they're not forbidden from returning items across the river, but then someone lets the fox and the chicken stay on the same side and it all goes pear-shaped.
• A variant appears in a training simulation the spies undergo in the Totally Spies! TV movie.

Real Life

• These types of games test ''means-end analysis,'' or the ability to set up sub-goals to reach an ultimate goal, even if those sub-goals appear contradictory to the ultimate goal. These type of logic games are useful in the world of artificial intelligence, where they're known as "toy problems" and are used to test methodologies and algorithms. A similar game, "missionaries and cannibals," has been used in the field of A.I. to demonstrate problem representation.

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