math
posted by emma on .
Three boxes of fruit are labeled Apples, Oranges, and Apples and Oranges. Each label is wrong. By selecting just one fruit from just one box, how can you determine the correct labeling of the boxes?

pick a fruit from the box labeled Apples and Oranges. Because all the labels are wrong, you know the box is either all apples or all oranges.
If you draw an apple, you know that the box is all apples. So, the box labeled Oranges must be not oranges, but apples and oranges, since it cannot be oranges (since its label is wrong), and you have an apple.
The remaining box, labeled Apples, must be all oranges.
reverse the logic if you draw an orange.