Fruit Crate Problem

First, start with the box labeled "apples and oranges". You know they are all mislabeled, so whichever fruit you pull out of this box is the only thing that can be inside. You pull out an apple!

Now that we have pulled out an apple from the mixed box we know it can only be apples. We have two boxes left. The boxes stating "oranges" cannot actually contain oranges since they are all mislabeled. 

Finally, the box labeled apples must actually be oranges since none of the labels are correct. 

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You can enjoy all of your delicious fruit!

Three mislabeled crates. One has apples, one has oranges, and one has both apples and oranges. All three are incorrectly labeled. By only pulling out one fruit, without looking into the box, how do you solve this dilemma?

Now we know the boxes labeled oranges must actually be the mixed box since it is not labeled correctly and cannot contain apples as we already know the other box is actually apples. This leaves one box left!