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 Solution To The Generalised Case
by K Sengupta)
Let us amend the condition (2) of the original problem, so that one of the digits in the minutes section is the pth root of the other digit in the minutes section, where p is a rational number.
Then, in conformity with the condition (3), we obtain mm = 48 as an extra value compared with the corresponding values obtained in terms of the earlier post.
This gives hh = 60-48 = 12 in terms of condition (1).
However, hh:mm = 12:48 violates condition (3) since 4+8 = 12, which is NOT the reversal of 12.
Consequently, no additional time (apart from 21:39) is possible for this case as well.
Edited on April 14, 2008, 12:37 pm