mathematics - Coin weighing problem

You are given ten stacks of golden coins, each stack consisting of ten coins and a digital scale with arbitrary precision.

You know that all stacks of coins are made from gold, weighing 10 grams per coin except one stack, which is made from silver but is painted golden. A silver coin weighs 1 gram less than a golden one, which makes its weight 9 grams.

With only being able to weigh exactly once, how can you identify the stack containing the silver ones?

Answer

1. You can number stacks from 1 to 10.


2. From each stack take as many coins as the stack number.


3. Weigh them all.


4. Subtract the weight from 10+20+...+100=550. The result is the number of the silver stack.

P.S. You can do the same even if you have 11 stacks of 10: just number them from 0 to 10.