In a medical office there are three boxes with medical supplies. The first box contains syringes, the second box contains needles, and the third one contains both syringes and needles. Each box is labeled – one says “syringes”, one says “needles”, and one says “syringes and needles”. However, it is known that none of the boxes are labeled correctly. How can you label the boxes correctly if you can take only one item from only one box and look at it?

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Answer: Take an item from the box marked “syringes and needles”. Suppose the item you take is a syringe. Then that box must be the box containing just syringes. Therefore, the box marked “needles” can’t be the box containing just syringes, and it can’t be the box containing just needles either — so it must be the box containing syringes and needles. The remaining box is therefore the box containing just needles.

If the item you take out is a needle, the solution is derived in a similar fashion: the box marked “syringes and needles” is the box containing just needles; the box marked “syringes” is the box containing both syringes and needles; and the box marked “needles” is the one containing just needles.


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