The hour, minute, and second hands of a clock with continuous sweeping can never be spaced at exactly 120° intervals. This was shown in Part 1

Find the exact time when these angles are as close as possible and the order of the hands are hour, minute, second in a clockwise fashion.

['As close as possible' means the sum of the individual deviations from 120° is minimized.]

I have not followed Charlie's derivation in detail, but he seems to propose 02:54:34 and 09:05:25 as approximate solutions.  As I read the specs, the solution must satisfy the condition not only of approx equal angles but also "and the order of the hands are hour, minute, second in a clockwise fashion."  I assume "clockwise fashion" means that the clock runs to the right hand (not "backwards"), and visually starting at 00:00:00 the hour hand comes first, then 120 degrees later the minute hand, and then a further 120 degrees later the second hand.  In Charlie's main solution the minute hand is after the second hand; and in the reflection (?) solution,  the hour hand is after both the minute and second hands.  

How is the "order of the hands" constraint being interpreted?

 

Posted by ed bottemiller on 2009-04-13 16:45:59