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If you count noon as one of the times (it just passed it), then 11 times between noon and midnight. At midnite, the minute hand has just gotten to the 12 position. It will happen every 65 minutes 27.27 seconds. Here are the times:

  1. 12:00:00 noon
  2. 1:05:27
  3. 2:10:55
  4. 3:16:22
  5. 4:21:49
  6. 5:27:16
  7. 6:32:44
  8. 7:38:11
  9. 8:43:38
  10. 9:49:05
  11. 10:54:33

If you do not count either noon or midnight since you want between, then it is 10 times.

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Q: How many times does the minute hand pass the hour hand between noon and midnight?
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