A meeting started after 1 o'clock but before 12 o'clock according to a wallclock( which does not have separate second marks and minute marks) mounted on a wall of the meeting room. At the precise instant of commencement of the meeting, the second hand ( the clock hand which measures seconds) was situated exactly on a minute mark and a prime number of minute marks ahead of the hour hand.

The 24 Hour electronic wristwatch, belonging to the Chairman who had synchronised his watch in accordance with the wallclock, displayed precisely AB:CD Hours( in HH:MI format ) at the same instant, where the number ABCD in the decimal system corresponds to a perfect square. (ABCD may or may not contain leading zeroes).

Determine the precise time of commencement of the meeting in accordance with the Chairman's wristwatch.

(In reply to Solution, or misinterpretation? by tomarken)

If the clock's hands move, not in a quantum-like manner but fluid, then the only time the hour hand (and minute hand) would be on a minute mark would be when the second hand is exactly on the 12.  A reference to the minute hand is therefore not needed.  The answer 3:24 is correct as 0324 is a perfect square and the hour hand is exactly 43 -- a prime number -- minute marks from the second hand. 

Posted by Dej Mar on 2006-03-18 17:49:55