Which is right more often, a stopped clock or a slow one?

Question

You have two broken 12-hour clocks. The first has stopped completely. The second still runs but loses one minute every day. Which clock shows the correct time more often? Justify with actual counts.

Accepted Answer

The stopped clock, by a wide margin. The stopped clock shows one fixed time. On a 12-hour dial the true time passes through that reading twice a day. So the stopped clock is exactly right twice every day. The slow clock loses one minute per day. It is right only when its error is a whole number of 12-hour cycles, that is, when it has lost 720 minutes. That takes 720 days. So it is exactly right once every 720 days, roughly every two years. Twice a day beats once every two years by a factor of about 1,440. A softer version. If you count "close enough" rather than exactly right, say within a mi…

Which is right more often, a stopped clock or a slow one?

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