Math Quiz: All around the clock

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At 12 o'clock the minute hand and the hour hand of an analogue clock point to the same position. This happens at other times as well. Can you figure out a rule for calculating those times?

Additionally, it may also be possible that all three hands (hours, minutes and seconds) overlap. When does this happen?

Note: This clock-riddle is pretty close to the relationship between day length, the length of a whole year and the duration of a single turn of the rotating earth.

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