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)

I concur with your logic and your answer.  I wanted to add that the second hand will be vertical every time the hour hand moves to the next minute mark.  Thus at 3:24, the hour hand will be on the 17th minute, and the second hand will be 43 marks away - another prime number.

Addendum: 19:36 is also available, but would have the hour hand on the 38th minute mark, the minute hand on the 36th and the second hand on the 0th/60th minute mark and thus does not provide a solution.

Posted by Leming on 2006-03-16 18:30:08