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OT Analog clock math problems

Posted By: joe freedman
Date: Tuesday, 4 May 2010, at 2:22 a.m.

In Response To: OT Analog clock math problems (Jason Lee)

I think the answer to #1 is 22, assuming that the both hands move continuously.

On the second problem, perhaps it can be divided into parts. First, how often do the hour and minute hands form a 120 degree angle? I'd guess that's also 22.

Then, of those 22 times, how often is the second hand exactly between the hour and minute, on the outside of their angle? At most 22. But the position of the second hand affects the position of the minute hand. So the second hand won't necessarily be 120 degrees away from the other two hands when they are 120 degrees apart. For example at 4 and 8 o'clock, the second hand must be at the 12 in order for the minute and hour hands to be 120 degrees. At the other more "irrational" times, maybe the minute hand could be 120 degrees away, but that would seem to require higher math to solve.

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