Ten stacks of coins, one stack fake

Question

You have 10 stacks of coins, each stack containing at least 10 coins. Nine stacks are genuine, each coin weighs exactly 10 grams. One stack is entirely counterfeit: each of its coins weighs 9 grams (1 gram light). You have a digital scale that reads exact weight (not a balance), but you may use it only once. Identify the counterfeit stack with a single weighing.

Accepted Answer

The trick is that a digital scale returns a number, so you can make each stack contribute a distinguishable amount to the shortfall. The weighing. Number the stacks 1 through 10. Take: - 1 coin from stack 1, - 2 coins from stack 2, - 3 coins from stack 3, - …, - 10 coins from stack 10. Place all 1 + 2 + \cdots + 10 = 55 coins on the scale together. Expected vs. actual. If every coin were genuine (10 g each), the total would be 55 	imes 10 = 550 	ext{ grams}. But the counterfeit stack's coins are each 1 g light. If stack k is the fake, you placed k of its coins on the scale, so the reading f…

Ten stacks of coins, one stack fake

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