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?
We know that hour hand and the minute hands are coincident on 12*T/11 minutes past T o'clock, where T = 0, 1, 2, 3, ...., 10
(where 12 0'clock is denoted by 0)
A separate examination of all the 11 cases would reveal that the second hand will be be situated at the place of coincidence of the hour hand and the minute hand only when T=0.
Thus, there do not exist any other time apart from 12:00:00 when all the three hands will be coincident.
Solution
