9. 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?

The box with "Apples only" will be mistakenly labeled AO or O.
The box with "Oranges only" will be mistakenly labeled AO or A.
The box with "Apples and  Oranges" will be mistakenly labeled O or A.
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If I stand in front of the box mislabeled O, I know that it is actually box AO or A.
If I stand in front of the box mislabeled A, I know that it is actually box AO or O.
If I stand in front of the box mislabeled AO, I know that it is actually box A or O.
If I choose either the A or O box, withdrawing the piece of fruit will be insufficient information because seeing either fruit will not tell me that I have the box with that one fruit or both fruits.
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The only box where seeing the fruit will tell me the contents conclusively is the box mislabeled AO.
If I withdraw an apple, then the box mislabeled AO can be correctly labeled A.
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Upon determining the contents of that one box, I can determine the contents of the other 2 boxes.
If box AO is now A, then I know that box O cannot be A (we already have A) and must be box AO.
The last box must be O.
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