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HINT: The answer is NOT 24.

See Answer

ANSWER: 22.

EXPLANATION: At first glance, it might seem that the hour hand and minute hand overlap every 60 minutes, but they actually overlap every 65 minutes and 30 seconds for a total of 22 overlaps. Beginning at 12:00, the hands overlap at the following times: 12:00, 1:05, 2:11, 3:16, 4:22, 5:27, 6:33, 7:38, 8:44, 9:49, and 10:55 both in the am and pm. Note that between 11:00 and 12:00, the hands do not overlap.

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