You have 10 bags of gold coins. 9 of the bags contain genuine coins weighing 10 grams each, but 1 bag contains fake coins weighing 9 grams each. You have a digital scale that gives exact weight readings in grams, but you can only use it ONCE. How can you identify the bag with the fake coins?
Take 1 coin from Bag 1, 2 from Bag 2, 3 from Bag 3, up to 10 from Bag 10. Weigh all 55 coins together. Subtract the total weight from 550 grams.
If all coins were real, 55 coins would weigh 550g. Each fake coin reduces the total weight by 1g. The deficit in grams equals the number of fake coins on the scale, which directly corresponds to the bag number.
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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