History Main / ThreePlusFiveMakeFour

Maths nerd bit: You're looking for the smallest ''x'' and ''y'' that satisfy 3''x''−5''y''=4; then fill the 3-liter ''x'' times, pouring it into the 5-liter when full, and emptying the 5-liter when it's full (which you'll do ''y'' times). The solution is ''x''=3 and ''y''=1. The alternate solution up there is the dual formulation, 5''x''−3''y''=4 (''x''=2, ''y''=2). From here, two details present themselves: one, that it's easily adaptable to other values other than 3 and 5, and two, that a solution exists only if the target value is either a factor or a multiple of the highest common factor of the container sizes (e.g. you can't get 4 liters from 6- and 3-liter containers).

A slightly simpler solution is:
# Fill the 5-liter container.
# Fill the 3-liter container from the 5-liter container, leaving 2 liters.
# Fill the 5-liter container, then use it to fill the 3-liter container (which already has 2 liters in it, so only needs one more liter to fill it, leaving 4 liters in the 5-liter container.

This puzzle dates back at least as far as the 1920s, and quite possibly earlier still.

# Refill the 5-liter, then fill the 3-liter from the 5-liter container. Leaving 4 liters in the 5-liter container.

You have two containers, one that holds 3 liters and one that holds 5 liters, and access to a water source. Place exactly 4 liters of water into a third container (one that holds at least 5 liters, so that you can't simply fill the container to the brim and be done with it).

* This puzzle and several variants appear in the ''VideoGame/ProfessorLayton'' series. In ''VideoGame/ProfessorLaytonAndTheCuriousVillage'', the puzzle "Water Pitchers" asks you to divide a 16- and 9-quart/litre pitchers until they each hold 8 quarts/litres of water.

!!Examples

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[[AC:Video Games]]

[[quoteright:300:[[VideoGame/ProfessorLayton https://static.tvtropes.org/pmwiki/pub/images/water_pitchers_1.png]]]]

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%%* Appears in ''VideoGame/RuneScape'', among other {{Stock Puzzle}}s.

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* ''TabletopGame/PerplexCity'' used this one on a card.

* In the movie ''Film/DieHardWithAVengeance,'' the two main characters must solve this type of puzzle in order to disarm a bomb near a public fountain.
** [[WhatCouldHaveBeen In the original script]], the bomb was a ChekhovsGun, as the movie would end with [=McClane=] planting the bomb on the bad guy's helicopter, and upon discovery one of them [[GallowsHumor asks]] [[BrickJoke if anyone has a four gallon jug]] (in the final script the bomb was used for something else entirely without the puzzle being brought up again).
* The problem appears, at first, to be included in an I.Q. Test in ''Film/{{Idiocracy}}'', but as the world is inhabited by morons the actual question is, how many buckets do you have?

* This puzzle appears in ''VideoGame/KnightsOfTheOldRepublic'' on Manaan, and solving it is a prerequisite for the "good" ending on that planet.
* This puzzle and several variants appear in the ''VideoGame/ProfessorLayton'' series.
* A slight variant with different values in ''VideoGame/ZorkZero'', a game almost entirely composed of [[StockPuzzle stock puzzles]].

* An apparently more complex version of this classic puzzle appears at the end of ''VideoGame/SherlockHolmesVersusArseneLupin'', where you have to measure exactly 478cc of black powder with only 250cc, 80cc and 12cc containers at your disposal. I say apparently only, because [[spoiler:1×250 + 19×12=478, so you don't actually have to use the pour-bigger-into-smaller subtraction trick at all to solve it]].
** [[spoiler:It ''can'' be done much faster with the pour-bigger-into-smaller trick, though: 1x250 + 3x80 − 1x12=478.]]
** The original version also appears in "Sherlock Holmes and the Mystery of the Mummy" as well as "Sherlock Holmes and The Mystery of the Persian Carpet" (Which borrowed every other puzzle too)

* Appears in ''VideoGame/RuneScape'', among other {{Stock Puzzle}}s.
* Appears in ''{{Videogame/Phantasmat}}'' as an unusual method of switching on a generator.
* Done with [[spoiler: lava]] in the last chapter of the Wii ''Franchise/CarmenSandiego'' game.

* In ''[[Creator/ZapDramatic Sir Basil Pike Public School]]'', if you pick the boy's path, you must solve this puzzle for the janitor before heading to the tennis court. (The girl's path has a KnightsAndKnaves puzzle instead.)
* The final level of ''VideoGame/TombRaiderTheLastRevelation'' contains this exact puzzle and two variants.
* ''VideoGame/TheCave'' also has this puzzle but in a twist, or perhaps just an [[SolveTheSoupCans acknowledgment that such puzzle in video games are a waste of time]], the game also gives you a URL where the player can simply find the answer to the puzzle.
* This is done with medicine for a sick elephant in one of the 12 minigames of the edutainment game ''Maths Circus''. This minigame is remade in ''Math Circus Act 4'', throwing in multiple types of medicine that should not be mixed with the others.

[[quoteright:350:[[VideoGame/MathsCircus https://static.tvtropes.org/pmwiki/pub/images/math_circus.png]]]]
[[caption-width-right:350:Or, in this case, 3 + 4 = 1]]

* This is done with medicine for a sick elephant in one of the 12 minigames of the edutainment game ''Math Circus''. This minigame is remade in ''Math Circus Act 4'', throwing in multiple types of medicine that should not be mixed with the others.

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* The problem appears, at first, to be included in an I.Q. Test in ''Idiocracy'', but as the world is inhabited by morons the actual question is, how many buckets do you have?

[[''AC:{{VideoGames}}]]

* The problem appears, at first, to be included in an I.Q. Test in Idiocracy, but as the world is inhabited by morons the actual question is, how many buckets do you have?

[[''AC:VideoGames]]

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* The problem appears, at first, to be included in an I.Q. Test in ''Film/Idiocracy,'' but as the world is inhabited by morons the actual question is, how many buckets do you have?

[[AC:VideoGames]]

* ''VideoGame/RustyLake Hotel'' has a puzzle like this, in order to pour a certain amount of water into a flask, for use in a distiller nearby.

The solution is as follows:
#First, fill the 3-liter container to the brim.
#Pour the 3 liters of water into the 5-liter container.
#Fill the 3-liter container again.
#Pour water from the 3-liter container into the 5-liter container until it is filled to the brim. This should leave you with 1 liter of water in the 3-liter container.
#Empty out the 5-liter container, then pour the 1 liter of water into it from the 3-liter container.
#Fill the 3-liter container once more, then pour the water from both containers into the third container.

An alternate solution with fewer fills:

* In the movie ''Film/DieHardWithAVengeance,'' the two main characters must solve this type of puzzle in order to disarm a bomb near a public fountain.\\
[[WhatCouldHaveBeen In the original script]], the bomb was a ChekhovsGun, as the movie would end with [=McClane=] planting the bomb on the bad guy's helicopter, and upon discovery one of them [[GallowsHumor asks]] [[BrickJoke if anyone has a four gallon jug]] (in the final script the bomb was used for something else entirely without the puzzle being brought up again).