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)

Though I agree with the conclusion, and in general the analysis presented, one of the possible values of mm in conformity with condition (ii) is 00. 
If single digit values of the hours are permitted and can be considered the reversal of themselves or if zero-leading digits as hours are permitted, then 00 also conforms with condition (iii) giving a time-value of 0:00 or 00:00 (=> 24:00).
Of course, this time does not conform to condition (i), from which it, along with all but one of the other given possibilities from conditions (ii) and (iii), may be eliminated.

Posted by Dej Mar on 2008-04-11 02:42:58