Two boys, a tiny boat and twenty soldiers

Question

Twenty soldiers arrive at a river and find two boys playing in a small rowing boat. The boat can carry either two boys, or one soldier, but not a soldier and a boy together. Everyone can row.

The soldiers must all get across, and afterwards the two boys must be back together with their boat on the side where they started, so they can carry on playing.

How many one-way crossings does the whole operation take?

Accepted Answer

Eighty crossings. One soldier's cycle. Both boys are on the near bank with the boat. 1. Both boys row across. 2. One boy rows back. 3. A soldier rows across. 4. The other boy (who waited on the far bank) rows back. After these four crossings, one soldier is across, and both boys and the boat are back on the near bank, exactly as at the start. Nothing else moved. Twenty soldiers. Repeat the cycle twenty times: 20 × 4 = 80 crossings. After the last cycle the boys are home with their boat, as required. Why no shortcut exists. Each soldier needs a crossing of his own, and the boat can only return…

Two boys, a tiny boat and twenty soldiers

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