A merchant has 10 sacks of gold coins, each containing 10 coins. Nine of the sacks have coins weighing 10 grams each, but one specific sack has counterfeit coins weighing 9 grams each. Using a digital scale that provides an exact numerical weight in grams, what is the minimum number of weighings required to identify the fake sack?
1 weighing
Take 1 coin from sack 1, 2 coins from sack 2, 3 from sack 3, and so on up to 10 coins from sack 10. Weigh all 55 coins together. If all coins weighed 10 grams, the total expected weight would be 550 grams. Subtract the actual measured weight from 550; the resulting difference directly tells you the number of the fake sack (e.g., if it's 4 grams short, sack 4 is the fake one).
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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