Puzzle
There are three boxes, one contains only apples, one contains only oranges, and one contains both apples and oranges. The boxes have been incorrectly labeled such that no label identifies the actual contents of the box it labels. Opening just one box, and without looking in the box, you take out one piece of fruit. By looking at the fruit, how can you immediately label all of the boxes correctly?

Question

Puzzle

There are three boxes, one contains only apples, one contains only oranges, and one contains both apples and oranges. The boxes have been incorrectly labeled such that no label identifies the actual contents of the box it labels. Opening just one box, and without looking in the box, you take out one piece of fruit. By looking at the fruit, how can you immediately label all of the boxes correctly?

Accepted Answer

Open the box that is labeled "Apples and Oranges".
You know that since none of the labels are correct, the box must either contain only apples, or only oranges.
Suppose that you remove an apple from that box. Therefore, that box is the "Apples Only" box. (If, in fact, you removed an orange from the box, you can swap “Apples” and “Oranges” for the rest of the description; the same reasoning applies).
One of the two remaining boxes must be the "Oranges Only" box. The remaining two boxes are labeled "Apples Only" and "Oranges Only". Since the labels cannot match, the “Oranges Only” label cannot have “Orange Only” contents.
Therefore, the one labeled "Apples Only" is the box that contains only oranges, and the box labeled "Oranges Only" is the box that has both kinds of fruit.

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