A clock that strikes six in five seconds

Question

A grandfather clock strikes the hour. At six o'clock, the time from the first strike to the sixth strike is exactly 5 seconds. The strikes are evenly spaced and each strike is instantaneous.

How long does the clock take to strike twelve?

The instinctive answer, 10 seconds, is wrong.

Accepted Answer

11 seconds. Count gaps, not strikes. Six strikes have five gaps between them: strike, gap, strike, gap, strike, gap, strike, gap, strike, gap, strike. Those five gaps take 5 seconds, so each gap is 1 second. Twelve strikes have eleven gaps, so from the first strike to the twelfth takes 11 × 1 = 11 seconds. Why 10 is tempting. Doubling the number of strikes feels like it should double the time. But the time is measured between the first and last strike, which counts the gaps, and going from six strikes to twelve takes the gaps from five to eleven, not from five to ten. Whenever a puzzle counts…

A clock that strikes six in five seconds

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