You have 10 bags of gold coins. Each bag contains 10 gold coins. In nine of the bags, all the coins weigh 10 grams. However, in one of them, each coin weighs 9.9 grams, i.e. 0.1 gram less than 10 grams. You are given a highly accurate weighing machine that can tell you the weight of an object placed on it, correct to a 100 th of a gram. However, you only have enough money to use it once. How can you find out which bag has the defective coins?
Solution is here