Five identical-looking bags contain coins. Four bags contain genuine gold coins weighing 10 grams each, but one bag contains counterfeit coins weighing 11 grams each. You have a digital scale that gives exact weight readings, but you can only use it ONCE. What is the minimum total number of coins you must draw from the bags to identify the counterfeit bag?
10 coins.
Number the bags 1 through 5. Take 0 coins from Bag 1, 1 coin from Bag 2, 2 from Bag 3, 3 from Bag 4, and 4 from Bag 5 (totaling 10 coins). If all were genuine, they would weigh 100g. Every extra gram above 100g indicates which bag contains the 11g coins (0 extra grams = Bag 1, 1 extra gram = Bag 2, etc.). The minimum sum of 5 distinct non-negative integers is 0+1+2+3+4 = 10.
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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