A square sheet of paper is folded exactly in half, and the folded piece is then folded exactly in half again the other way, giving a small square that is four layers thick. One hole is punched right through all four layers. How many holes are seen when the sheet is opened out flat?

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4. One punch pierces every layer, so the number of holes equals the number of layers. Two folds give 2 × 2 = 4 layers, hence 4 holes. The traps: 2 counts the folds instead of the layers, 8 doubles the layers once too often, and 1 forgets that the punch goes through the whole packet.

A square sheet of paper is folded exactly in half, and the folded piece is then folded exactly in half again the other way, giving a small square that is four layers thick. One hole is punched right through all four layers. How many holes are seen when the sheet is opened out flat?

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