What times of the day are the hour hand and minute hand of a clock both exactly on consecutive minute marks?
Since hour hand moves precisely 1 minute Mark every 12 minutes, it follows that:
At precisely 12*R minutes past T o'clock; the hour hand is situated at (5T+R) minute mark ahead of 12 hr. Mark and the minute hand is situated precisely 12*R minute Mark's ahead of 12 Hr. mark. It is obvious that: R=0,1,2,3,4,5 and T=1,2,3...., 12 ..........(i)
Accordingly, we must have: 5T+R-12R=+/-1 => 5T-11R= +/-1
If, 5T-11R=1, then in consonance with constraints on R and T given in (i), we have:
T=9 and R =4 => 12*R=48
If 5T-11R = -1, then we have T=2, R=1 => 12*R = 12
Consequently, the required times are:
2:12 and 9:48
Edited on January 12, 2022, 1:16 am
Puzzle Solution
