How many times a day do the hands of a clock overlap?

Over the course of a day, the hour and minute hands of your men's watch will overlap, but have you ever wondered how many times a day the hands of a watch overlap? This question is out of the ordinary and that's why we decided to look into it. While some may instinctively want to answer 24 as the number of hours in the day, this is not the correct answer. Even if it is tempting to think that at each hour the hands meet you will see that the answer is quite different. In reality, the hands of a watch overlap 22 times. Before I give you an explanation, you can visualize a watch face to guide you. The hands of a quartz or automatic watch overlap at :

• 12h00
• 1h05
• 2h10
• 3h15
• 4H20
• 5h25
• 6h30
• 7h35
• 8h40
• 9h45
• Et 10h50

The hands overlap at the above times and this situation occurs twice, once in the morning and once in the day/evening. The hands therefore overlap 22 times a day. This number corresponds to the coincidence of the watch hands twice a day. You can also notice that at 11:55 the hands do not overlap. Indeed, at this time, the hour hand moves to 12 o'clock, when the minute hand is at 11 o'clock.

Why don't the hour and minute hands meet at 11:55? Concretely, the hands do not really overlap at 1:05, 2:10, 3:15, etc.  Indeed, when the hour hand arrives at 1, five minutes later, the minute hand arrives at 1. But the hour and minute hands do not quite meet because the hour hand will have moved 1/2 of the distance between 1 and 2. Therefore, the exact time when the two hands meet actually occurs a little after 1:05. The same situation occurs for the other hours where the hands overlap as indicated above: at 2:10, 3:15, 4:20, and so on. It is finally this cumulative shift that leads to the fact that at 11 o'clock, the minute hand meets the hour hand at 12 o'clock. Thus, over a period of 12 hours, the hands will overlap only 11 times. More precisely, if we do not take into account this cumulative shift, the hands overlap every 1 hour and 5, 454 545 minutes.