You have 12 identical-looking coins. Eleven are genuine, but one is counterfeit and has a slightly different weight (either lighter or heavier). What is the minimum number of weighings on a balance scale needed to guarantee identifying the fake coin AND determining whether it is heavier or lighter?
3 weighings.
A balance scale has 3 outcomes per weighing (left heavy, right heavy, balanced). 3 weighings yield 3^3 = 27 possibilities. Since there are 24 potential states (12 coins × 2 weight possibilities), 3 weighings are mathematically sufficient to isolate the counterfeit coin and its relative weight.
About this riddle
Logic riddles give you a few facts and ask what must be true. List what you know, cross out what cannot be, and see what is left.
Difficulty: Hard. More like this: Logic riddles with answers or try Einstein's Logic Grid for a different kind of puzzle.
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