How many times per day do the clock hands overlap ?

While some might instinctively answer 24, like the number of hours in a day, that's unfortunately not the correct answer. Even though it's tempting to think that the hands of the clock meet every hour, you'll see that the answer is quite different.

In reality, the hands of a clock overlap 22 times. Before giving you an explanation, you can view a dial of watch to guide you. The needles thus overlap at:

• 12:00
• 1:05
• 2:10
• 3:16
• 4:21
• 5:27
• 6:32
• 7:38
• 8:43
• 9:49
• And 10:54

The hands overlap at the hours above and this situation occurs twice, once in the morning and once in the day/evening, so 22 times a day! You can also notice that at 11:55 the hands do not overlap. Indeed, at this time, the hour hand moves towards 12 o'clock, while the minute hand is still at 11 o'clock.

Why don't the hour and minute hands meet at 11:55? In practice, the hands do not actually overlap at 1:05, 2:10, 3:15, etc. Indeed, the hour hand will gradually gain more ground on the minute hand. For example, at 4:20, the hour hand will be pointing towards 5 o'clock while the minute hand will still be at 4 o'clock.

It is the accumulation of this discrepancy that prevents the hands from overlapping at 11:55. At this time, the hour hand will already be positioned at 12 o'clock.