Counterfeit Coins
When we have an answer to a problem, we sometimes miss that there is a better solution. This puzzle demonstrates the point very well:
You have ten stacks of coins, each consisting of ten gold coins. One entire stack — you do not know which one — is counterfeit. You do know the weight of a genuine coin and you also know that a counterfeit coin is one gram overweight. You may weigh the coins on a digital weighing machine or a spring balance. What is the minimum number of weighings necessary to determine which stack is counterfeit?
Whatever answer you are given, keep on asking the class if they can do it in a smaller number of weighings until they give up or get down to one weighing.
Solution
