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Geometry

How many times does the minute hand of a clock overlap with the hour hand from 10am to 12am?

Answer

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June 16, 2012 2:47PM

23 times in all.

Note that from 11:00 to 11:59 (am or pm) the hands can never overlap. Thus from 10am to 11:59am, the hands will overlap just once at around 10:54am. The hands will overlap again at exactly 12:00pm (noon). And from 12:01pm to 12:am (midnight) the hands will overlap another 11 times.

The following times are the approximate overlapping times.

  1. 10:54am
  2. 12:00pm (noon)
  3. 1:06pm
  4. 2:11pm
  5. 3:16pm
  6. 4:21pm
  7. 5:27pm
  8. 6:32pm
  9. 7:38pm
  10. 8:43pm
  11. 9:49pm
  12. 10:54pm
  13. 12:00am (midnight).