An eccentric monarch has 10 sacks of gold coins, each containing 10 coins. Nine sacks contain genuine coins weighing exactly 10 grams each, but one single sack contains counterfeit coins weighing 9 grams each. Using a digital scale that provides an exact numerical weight in grams in a single weighing, how do you identify the counterfeit sack?
Take 1 coin from sack 1, 2 coins from sack 2, 3 coins from sack 3, and so on up to 10 coins from sack 10. Weigh them all together on the digital scale.
If all sacks were genuine, 55 total coins would weigh 550 grams. For every gram the total scale reading is less than 550, that corresponds to the number of the sack containing the 9-gram counterfeit coins (e.g., a deficit of 4 grams means sack 4 is fake).
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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