At a certain time I looked at a 24 hour digital clock and noticed some things about the time:
1)The number in the hours section plus the number in the minutes section makes 60.
2)One of the digits in the minutes section is the square root of the other digit in the minutes section.
3)The sum of the digits in the minutes section is the number in the hours section reversed.
What was the time?
(In reply to Puzzle Solution
by K Sengupta)
If the condition (ii) of the original problem, read as:
"One of the digits in the minutes section is the pth root of the other digit in the minutes section, where p is an integer > 1"
- then the valid mm values in conformity with this condition would be:
00, 11, 24, 42, 39, 28
mm=28 is ruled out, since this would yield an hh value of 42 in consonance with condition (i). This leads to a contradiction since hh<=23.
For the other five cases, it was proved in terms of the previous post that only hh:mm = 21:39 also satisfies all the three conditions.
Consequently, the only possible time for the general case is still 21:39.
Edited on April 11, 2008, 6:59 am