How many times each day do the minute and hour hands of a clock cross?
Explanations
22 times.
The two hands cross each other every 1 hour 5 minutes and 27 seconds. If the two hands would cross exactly every hour, then there would be 12 crossings in 12 hours. But they cross 5 minutes and 27 seconds “slower”. Thus, there are 11 crossings per 12 hours, starting with a midnight and counting their overlap as the 1st crossing of a day.
The next 12 hours start with the noon’s overlap, launching the second series of 11 crossings in the remaining half of the 24-cycle.