There are three boxes of fruits that are labeled as follows: “Apples”, “Oranges”, and “Apples and Oranges.” With the assumption that none of the boxes were labeled correctly, how would you re-label the three boxes correctly if you are only allowed to look at just one piece of the fruits from one of the three boxes.

Answer(1) If you select an apple, then the box that is labeled “Apples and Oranges” must contain just apples and should be re-labeled as such. The box that is labeled “Oranges” cannot contain just apples (since we already determined the box that contains just apples) nor just oranges (since all boxes are labeled incorrectly) and therefore the box must contain apples and oranges and should be re-labeled as such. The box that is labeled “Apples” must then contain just oranges and should be re-labeled as such.

(2) If you select an orange, then the box that is labeled “Apples and Oranges” must contain just oranges and should be re-labeled as such. The box that is labeled “Apples” cannot contain just oranges (since we already determined the box that contains just orages) nor just apples (since all boxes are labeled incorrectly) and therefore the box must contain apples and oranges and should be re-labeled as such. The box that is labeled “Oranges” must then contain just apples and should be re-labeled as such.

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