I have a very strange clock. At first glance, it looks like a normal clock with three hands and the numbers 1 through 12 all around. The only differences are that the hands are indistinguishable from each other and they are faster. One hand completes a circle in 3 minutes, another in 4 minutes, and the last in 6 minutes. They all go clockwise.

One morning, when I looked at the clock, the hands were all pointing exactly at the numbers 1, 2, and 3.
Later that day, I saw that the three hands were pointing exactly at 6, 10, and 11.

Can you identify which hands I saw each time? Prove it.

The 3-min hand moves +1/15 sec= +4/min
The 4-min hand moves +1/20 sec= +3/min
The 6-min hand moves +1/30 sec= +2/min
Therefore, all hands align with a number simultaneously at 1-min intervals.
If the 3-min hand starts at 2, then it will be on 10 after 5 minutes
If the 4-min hand starts at 3, then it will be on 6 after 5 minutes
If the 6-min hand starts at 1, then it will be on 11 after 5 minutes
Therefore, the solution is that the 3-min hand started on 2 and was then seen again on 10, the 4-min hand started on 3 and was then seen again on 6, and the 6-min hand started on 1 and was then seen again on 11

Posted by Gabe on 2004-02-17 13:03:22