In this Stock Puzzle, you are given a number of coins, or bags of coins, and a balance. You are told that one coin or bag is heavier or lighter than the others (in most versions of the puzzle, the odd-weight coins are counterfeit). Through a limited number of weighings, you must determine which coin or bag of coins is counterfeit.
Compare and contrast Needle in a Stack of Needles, when something is hidden amongst a slew of its duplicates. See 3 + 5 = 4 for another puzzle requiring math calculations on the spot; in this case, to redistribute a liquid between differently-sized containers to come up with a specific amount.
Examples:
Alternate Reality Games
- Perplex City: The "Poison Pill" card has a variant, where you must figure out how to identify pills of a different weight from five jars in one weighing.
- The Kindaichi Case Files: Kindaichi solves a ten-bags-of-coins variant almost immediately, necessitating him to explain the solution to a bewildered Miyako. The person who had posed the problem turns out to be the murder suspect, and she bemoans that she should have realized Kindaichi would see through her tricks given how casually he blew through the question.
- With a Tangled Skein: The Heroine has to solve this puzzle to find a certain soul disguised as a demon, out of the 12 demons. She only knows that, so initially does not realize how weight plays a factor. After some internal panic, she remembers that sin weighs souls, so a good soul will be lighter to drift to heaven. It doesn't work due to Satan, but things resolve regardless.
Live-Action TV
- Brooklyn Nine-Nine: In "Captain Peralta", Captain Holt asks the detectives a version of this, with twelve men on an island instead of coins and offers tickets to a Beyoncé concert for anyone who can solve it. Turns out that his own mentor asked him the same riddle and he couldn't figure it out, so he set the whole thing up so the detectives would find the answer for him.
- Drakensang 2 — The River Of Time: In order to open a chest, you're given several iron and lead weights and you must put the right number of them in the four boxes around the altar. If you can't find the solution, you can ask the druid Megalesios to solve it for you, but you won't gain any experience.
- Enchanter:
- In Spellbreaker, it appears using a spell that detects the power level of cubes. Naturally, the spell can be used only three times. And you don't know whether the correct cube will glow more or less than the fakes. Or only two times, if you take any of the treasure, making the puzzle and the game Unwinnable. The random number generator will be biased against you if you screw up.
- After three weighings, the game determines which coins might be the fake given the information you have, and if there's more than one possibility the game will switch it so that you have the wrong coin. Infocom was great.
- Fire Emblem: The Sacred Stones: Ewan presents this puzzle to Ross in a support conversation. However, in a slight twist, he doesn't ask how to do it in three weighings: he gives the more generic challenge of asking what is the minimum number of weighings required (and makes it 25 pebbles, not 12 coins). Ross immediately answers 24 (i.e., weighing the pebbles one by one), then after some encouragement from Ewan, answers 4. Close, but no cigar —the answer is still 3.
- Hotel Dusk: Room 215: During that time there are no important characters in the bar, you must solve one of these puzzles in order for them to appear.
- Professor Layton: Appears in a few different variants, usually involving weights rather than coins.
- Safe Cracker (1997): One puzzle involves a key-weighing machine that can only be used in two moves, in which the objective is to find one out of eight keys that's heavier than the others. Choosing the wrong key or making more than two moves scrambles the keys and resets the puzzle.
- Trouble in Terrorist Town: One traitor-exposing machine requires several people to be analyzed at once. This means that the player must find whom amongst them is the traitor.
- Virtue's Last Reward: There are four coins to weigh and a scale that gives you five weighings before resetting itself. As the weights of the coins are constant, and there are only four of them, the resetting is just a nuisance.
- Voyage: Appears in this Jules Verne-inspired adventure game, where you have to isolate the lightest of twelve 'isotopes' in the fewest number of steps, with varying points available depending on which of the above solutions you use.
Websites
- Ted: In the Counterfeit Coin Riddle
, you are an imprisoned mathematician who must earn freedom by determining which of twelve coins is counterfeit, using only a marker and three weighings on a scale.
