The Royal Mint
You are the treasurer in charge of the Royal mint, which produces a single type coin, the grote. There are ten machines producing grotes, one machine is producing grotes weighing one gram less than they should, each coin should weigh 10 grams. You have a set of broken scales which can be fixed to provide one single weigh of a single amount (no weight changes are allowed). Using the scales once you must identify the single faulty machine.
How do you do it?
Label the machines 1 thru to 10, take one coin from machine 1, 2 from machine 2 etc. However many grams you are out from you calculated total is the number of the machine producing the substandard coins.