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The hands do not overlap between 11 to 12, so only 22 overlaps per day.

--------------------------------- 1 of 2: Cjcarr2000 answer:

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It occurs 12 times a day

Overlap Time = Hour : (Hour * 5)

12:00, 1:05, 2:10, 3:15, 4:20, etc.

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2 of 2: Stormnoone answer:

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It occurs 22 times a day. (as Digbybare said, and not 24 as i was said at first)

Exact times = Hour : ( Hour * 65 / 12 )

that is, when it is "1:05", the hour hand has moved from '1' to '2' (that total distance is 5 minutes) as the minute hand has moved from '12' to '1' (that is exactly 5 minutes, or Hour * 5); so the Hour hand must has moved "Hour / 12" of the 5 minutes:

= Hour : [ (Hour * 5) + (Hour / 12) * 5 ]

= Hour : [ (Hour * 5) + (Hour * 5) / 12 ] => we take out the common (Hour * 5)

= Hour : [ (Hour * 5) * (1 + 1/12) ]

= Hour : [ (Hour * 5) * 13/12 ]

= Hour : (Hour * 65/12).

-------------------------

So the Successive exact time should be

1 : ~5.4

2 : ~10.8

3 : 16.25

4 : ~21.67

5 : ~27.08

6 : 32.5

......,and so on.

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Q: Imagine an analog clock set to 12 o'clock Note that the hour and minute hands overlap. How many times each day do both the hour and minute hands overlap How would you determine the exact times?
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