### How many times a day a clock’s hands overlap?

how many times in a day minute hand and hour hand overlap?

1. @Dave 22 times a day if you only count the minute and hour hands overlapping.

2. should be 24 times of the minute n hour hands !

3. @anonymous can you please explain..

4. If you start from 1 to 12 hours a day it overlaps 12 times and similarly for another 12 hours which makes it 24

5. @ Overlapping will occur when Lm = Lh +N, which means every N*(12/11) hours (for N = 0,1,2,3...). In other words, it will happen approximately every 1hr5mins27secs, starting at 00:00. In 24hours, this occurs a total of 24/(12/11) = 22..

6. The hour and the minutes clock coincide every 1 hr 5 min as u said but i think it happens 24 times as shown below:

OO:00, 01:05, 02:10, 03:15, 04:20, 05:25, 06:30, 07:35, 08:40, 09:45, 10:50, 11:55, 12:00, 13:05, 14:10, 15:15, 16:20, 17:25, 18:30, 19:35, 20:40, 21:45, 22:50, 23:55..this adds up to 24 times..will you please explain which cases your algorithm leaves from above.

7. @above here are overlapping times :
am
12:00
1:05
2:11
3:16
4:22
5:27
6:33
7:38
8:44
9:49
10:55

pm
12:00
1:05
2:11
3:16
4:22
5:27
6:33
7:38
8:44
9:49
10:55