Three mislabeled fruit jars

Question

There are three jars. One contains only apples, one contains only oranges, and one contains a mix of both. The jars are labeled APPLES, ORANGES, and MIXED, but you are told that all three labels are wrong.

You may reach into a jar (without looking inside) and pull out a single fruit, then look at it.

What is the minimum number of fruit you must draw to correctly relabel all three jars, and how?

Accepted Answer

The answer is one draw. The trick is choosing the right jar to draw from. Draw a single fruit from the jar labeled MIXED. Because every label is wrong, the MIXED jar is not mixed, it is pure apples or pure oranges. So one fruit reveals its true contents completely: - Suppose you draw an apple. Then the MIXED jar is actually the apples jar. Now finish by elimination. The jar labeled APPLES is wrong, so it is not apples; and it can't be the mixed jar's true content... let's be careful: - We've placed apples at the jar labeled MIXED. - The jar labeled ORANGES is wrong, so it isn't oranges; the o…

Three mislabeled fruit jars

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