SOLUTION: From 12:01 am on one day to 11:59 pm the same day, how many times do the hour and minute hands cross?

Question 246069: From 12:01 am on one day to 11:59 pm the same day, how many times do the hour and minute hands cross?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
It's a little counter-intuitive, but the answer is 21.

I looked at it from a real clock and wound it around manually.

Here's what I think is happening.

It crosses the hour hand roughly at the following times:

crossing  crossing time
1            1:06
2            2:11
3            3:17
4            4:22
5            5:27
6            6:33
7            7:38
8            8:43
9            9:49
10           10:54
11           12:00
12           1:06
13           2:11
14           3:17
15           4:22
16           5:27
17           6:33
18           7:38
19           8:43
20           9:49
21           10:54

That's 21 crossings.

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