How many times do hands of a clock coincide in a day?

The hands of a clock coincide 22 times in a day. Here's how:

1. In every hour, the minute and the hour hand coincide once. This is because the minute hand completes one full revolution (360 degrees) every hour, and during this time, the hour hand moves from one hour mark to the next. The two hands coincide when the minute hand "catches up" with the hour hand.

2. However, this doesn't happen 24 times in a day (once for each hour) because there is no coincidence at 12 midnight. The first coincidence happens just after 1 o'clock, not at 12 o'clock.

3. Therefore, during the 12-hour period from 12 midnight to 12 noon, there are 11 coincidences.

4. The same thing happens during the 12-hour period from 12 noon to 12 midnight. So, there are another 11 coincidences.

5. Adding these up, the hands of a clock coincide 22 times in a day.