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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. What is the minimum number of samples you need to label all of the boxes correctly?

Solution

You only need one sample to figure out how to label all the boxes. The solution depends on the key detail that all of the boxes are labeled incorrectly.

Suppose you pick from box labelled as Apple and Oranges and you got Apple from it. That means that box should be Apple as it is incorrectly labelled. So it has to be Apple box. Now the box labelled Oranges has to be mixed as it cannot be the Oranges box as they are wrongly labelled and the box labelled Apple has to be Oranges.