How many times per day do a clock's hands overlap?

The hands overlap every 12/11 hour.  So here are the times that they
overlap:

1.  midnight
2.  1 + 1/11 am
3.  2 + 2/11 am
4.  3 + 3/11 am
5.  4 + 4/11 am
6.  5 + 5/11 am
7.  6 + 6/11 am
8.  7 + 7/11 am
9.  8 + 8/11 am
10. 9 + 9/11 am
11. 10 + 10/11 am
12. noon
13.  1 + 1/11 pm
14.  2 + 2/11 pm
15.  3 + 3/11 pm
16.  4 + 4/11 pm
17.  5 + 5/11 pm
18.  6 + 6/11 pm
19.  7 + 7/11 pm
20.  8 + 8/11 pm
21. 9 + 9/11 pm
22. 10 + 10/11 pm

If midnight is considered part of both days, then the answer is 23 times.
Otherwise the answer is 22 times.