Here are three large burlap sacks, each tied at the mouth. Each sack has a label. One says baseballs, the next says grapefruit, and the third one says baseballs and grapefruit. The bags contain these things, all right, but the labels have been mixed up so that each label is wrong. You are allowed to point at one bag. I will open the bag and pull out one thing from the bag and show it to you. If you are clever in picking the sack to point at, you will learn enough from what I show you so that you'll be able to switch the three labels so they are all correct. Tell which bag you will point at and show why your solution works.
Solution
Point at the sack labeled baseballs and grapefruit. Whatever I show you is what's in the sack; that is, if I show you a baseball, then you can label that sack baseballs. The sack labeled grapefruit must then be baseballs and grapefruit, because it cannot be either baseballs or grapefruit. The sack labeled baseballs must therefore be properly labeled grapefruit.
Backing up, if I show you a grapefruit, then you can label that sack grapefruit. The sack labeled baseballs must then be baseballs and grapefruit because it cannot be either baseballs or grapefruit. The sack labeled grapefruit must therefore be properly labeled baseballs.