How many times in a day do the two hands on a clock coincide?

The two hands on a clock coincide or overlap each other multiple times in a day. Specifically, the hour and minute hands overlap each other at exactly 12 o'clock (noon) and 12 o'clock midnight, forming a perfect overlap.

In addition to these two instances, there are also other times when the hands align partially or fully. Between 12 o'clock and 1 o'clock, the hands align once when the minute hand points to 12 and the hour hand points directly at one of the hour marks. Similarly, between 1 o'clock and 2 o'clock, there is another alignment when the minute hand points to the hour mark, and so on.

In total, the hands of a clock coincide or overlap 11 times in a 12-hour period (from 12 o'clock to 11 o'clock). Therefore, in a full 24-hour day, the hands of a clock coincide or overlap 22 times.