Time's Up - Futility Closet

Time’s Up

A perplexing question by the Soviet science writer Yakov Perelman:

If a clock takes three seconds to strike three, how long does it take to strike seven?

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Nine seconds. As the clock strikes three it’s marking two intervals, one between the first and second strikes and another between the second and third. If the three strikes unfold in three seconds, then each interval is 1.5 seconds long. In striking seven the clock marks six such intervals, so this takes 1.5 × 6 = 9 seconds. From Perelman’s For Young Mathematicians (1924), via Quantum, November-December 1992 (“Kaleidoscope,” pp. 32-33).