Clock Hands

When do the hour and the minute hands of the clock lie on top of each other, and also between the numbers 1 and 2?

One such time is around 1:05 – at 1 o’clock and 5.454… minutes. This can be easily found by solving the linear equation x = 12(x – 5) => x=60/11.

Another time you possibly didn’t think about is 12:00 o’clock. At that time, the hour and minute hands are on top of each other and just between the two digits of the number 12.

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