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?
(In reply to
solution by Charlie)
Well... Charlie... (and DJ),
We might assume that the hour, minute, and second hands are ALWAYS in a '60th of a circle' position. (That is, they don't swing smoothly, they 'jerk' 6 degrees when appropriate.) This is the behavior in many digital watches.
In other words... the hour hand stays pointing to the 12 until 12:12, at which time it points 6 degrees off of noon. At 12:24, it points to 12 degrees off of noon. At 12:36 it points to 18 degrees. At 12:48, it points to 24 degrees, and at 1:00 it points to 30 degrees (pointing to the one).
In this case, at 1:05, it would still be be pointing to 30 degrees.
The minute hand would 'jerk' forward every minute. So, at 1:05 it would reach the 30 degree mark.
The second hand would 'jerk' forward every second. So, at 1:05:05, the second hand would also reach the 30 degree mark.
And similarly, this would happen at the other conjunctions.
So, each of the 11 times (in a 12-hour period), the second hand would catch up to them. And in all 11 cases, we would have a 'conjunction' of the hands.
- SK
re: solution
