Answer Posted / kerobotz

After starting at 12am they don't meet back up at 1:05am
they actually meet back up at 1:05 and 27.27 secs. This
extra time adds up over the course of the morning and after
11 hours becomes 5 mins.

Therefore it is 22 times in a day.

The math:
min_hand completely rotates 1/hr
hr_hand completely rotates (1/12)/hr
They unite at time t when t(1-1/12)=1
==> t=1/(1-1/12)
=1/(11/12)
=12/11
==> t is 1.0909 hours

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