You have 10 sacks of gold coins. Nine of the sacks contain coins weighing 10 grams each, but one sack contains counterfeit coins weighing 9 grams each. You have a digital scale that provides an exact numeric weight in grams. What is the minimum number of weighings required to identify the counterfeit sack?
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Unlike traditional balance scale riddles that require 1 weighing using a spring scale by taking 1 from sack 1, 2 from sack 2, etc., a digital scale allows you to weigh a combination in a single go. 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. Place all these 55 coins on the digital scale at once. If all coins weighed 10 grams, the total weight would be 550 grams. Subtract the actual measured weight from 550; the resulting difference directly tells you the number of the counterfeit sack (e.g., if it weighs 547 grams, the difference is 3, meaning sack 3 is counterfeit).
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: Medium. More like this: Logic riddles with answers or try Einstein's Logic Grid for a different kind of puzzle.
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