The current time is between 1 o’clock and 12 o’clock in a wallclock and both the minute hand and the hour hand are situated precisely on two distinct minute marks. It is observed that the hour hand is a square number of minute marks ahead of the 12 Hour Mark . The number of minute marks by which the hour hand is ahead of the minute hand is a different perfect square greater than 1. Determine the current time from the information provided in the above statements.

It say's "It is observed that the hour hand is a square number of minute marks ahead of the 12 Hour Mark"

This means that the hour hand is at the 1, 4, 9, 16, 25, 36, 49 minute mark.  It also says that "The current time is between 1 o’clock and 12 o’clock". This means that the hour hand could not be at the one minute mark since that would not be a time between 1 and 12 o'clock. This means that the hour hand is at the 4, 9, 16, 25, 36, 49 minute mark.

My next assumption is that the the hour hand moves at a constant rate.  So when it says that "both the minute hand and the hour hand are situated precisely on two distinct minute marks."  For the hour hand to be percisely on a minute mark the minute has to be 0/5, 1/5, 2/5, 3/5, or 4/5 of the way around the clock.  This means that the minute hand has to be on the 0, 12, 24, 36, or 48 minute mark

Using these the only numbers that work are 16 and 12 (4 less) So the hour hand is at the 16 minute mark and the minute hand is at the 12 minute mark, making it 3:12

Posted by Whit on 2005-10-04 18:36:16