Six shots in sixty seconds

Question

A cowboy fires his six-shooter, all six shots, at a steady rhythm. The time between the first bullet and the last bullet is 60 seconds. At the same rhythm, how long would it take him to fire three shots? The instinctive answer, 30 seconds, is wrong.

Accepted Answer

24 seconds. Count the gaps. Six shots have five gaps between them (first to second, second to third, and so on up to fifth to sixth). Those five gaps take 60 seconds, so each gap is 12 seconds. Three shots. Three shots have two gaps: 2 × 12 = 24 seconds. Why 30 is tempting. Halving the shots feels like halving the time, but the time is measured between the first and last shots, which counts gaps, not shots. Halving six shots to three takes the gaps from five to two, not from five to two-and-a-half. This is the fencepost error: a fence with six posts has five rails. Relatives. A clock that tak…

Six shots in sixty seconds

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