At exactly 12:00, the hour, minute, and second hands are all pointing straight up.

Are there any other times that all three hands are superimposed?
If so, when?

Using the natural scale of angular measure of "clock face hours" the equations for all hands to point at the same place are
t=12t-12k=720t-12m where m and k are integers and t is "time." Hence 11t=12k and 719t=12m so 719k=11m and k=11j, m=719j since 719 and 11 are coprime. Thus t=12j where j is any integer. The time must be a multiple of 12.
Edited on February 1, 2004, 8:34 pm

Posted by Richard on 2004-01-30 12:35:46