Do the three hands on an analog clock (hours, minutes, seconds) ever divide the face of the clock into three equal segments, i.e. 120 degrees between each hand?

Using clock face hours as the angular unit, we have m=12*h and s=720*h, where h, m, and s are the angles of the hour, minute, and second hands. We are trying to get 12*h=h+/-4+12*k and 720*h=h-/+4+12*n for some integers k and n. After a little arithmetic, these lead to

3*(719*k - 11*n) = -/+730

which is impossible since 3 does not divide 730.

Edited on July 6, 2004, 12:52 pm

Posted by Richard on 2004-07-05 14:54:58