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.

As I understand the question, there could be many solutions:

The hour hand is on a "minute mark" - there being 5 minute marks per hour, each one represents 12 minutes.  Therefore, the times of day AB:CD where the hour hand is on a minute mark, and ABCD is a perfect square are 3:24, 4:00, 9:00, and 10:24.

Then, the second hand?  It has nothing to do with the second paragraph of the puzzle, and could be situated anywhere as long as it is a prime number of seconds past the hour hand...

IF, on the other hand (no pun intended), the first paragraph is asking about the minute hand instead of the second hand, then the time would be 3:24:

324 is a perfect square.
At 3:24 the hour hand would be on the 17th minute mark, and the minute hand would be on the 24th minute mark - 7 (a prime number) marks ahead of the hour hand.

Was the problem stated incorrectly, or am I just missing something?

Posted by tomarken on 2006-03-16 12:19:52