Three boxes are labeled as "Apples," "Oranges," and "Apples and Oranges." All the boxes are labeled incorrectly. You can pick one fruit from one box only. Which box do you choose to correctly label all boxes?ApplesOrangesApples and OrangesNo box
Question
Three boxes are labeled as "Apples," "Oranges," and "Apples and Oranges." All the boxes are labeled incorrectly. You can pick one fruit from one box only. Which box do you choose to correctly label all boxes?ApplesOrangesApples and OrangesNo box
Solution
You should choose the box labeled "Apples and Oranges". Here's why:
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Since all boxes are labeled incorrectly, the box labeled "Apples and Oranges" can't contain both fruits. It must contain either only apples or only oranges.
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Pick one fruit from the "Apples and Oranges" box. Let's say you pick an apple. This means the box must be the "Apples" box, because it can't be the "Oranges" box (as it's labeled incorrectly) and we've just proven it can't be the "Apples and Oranges" box.
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Now you have two boxes left: one labeled "Apples" and one labeled "Oranges". But you know these are also labeled incorrectly. So, the box labeled "Apples" must contain oranges, and the box labeled "Oranges" must contain both apples and oranges.
So, by picking a fruit from the "Apples and Oranges" box, you can correctly label all boxes.
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