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OT Analog clock math problems

Posted By: Nack Ballard
Date: Tuesday, 4 May 2010, at 5:22 p.m.

In Response To: OT Analog clock math problems (Nack Ballard)

Nobody has corrected my answer to Problem 2, so perhaps I lucked into the right one, but...

It seems to me that the 44 instances of +/- 120 for the hour/minute hands (over 24 hours) occur over 66 increments, where the hands line up (0 degrees) the third, sixth, ninth, etc., and the rest are the -120/+120 situations. Likewise, the 2832 instances of +/-120 for minute/second occur over 4248 increments, whereby the third, sixth, ninth, etc., are when the hands line up.

If so, then hour/minute/second line-ups will occur and two-way line-ups will occur with the third hand at +/-120 (and from the above conclusions it is possible to determine exactly when), but three-way 120 instances will never occur exactly. So, now I think the answer to problem 2 is zero.

Nack

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