Considering a positive whole number X which contains more than one digit, let us define R(X) as the number obtained by reversing the digits of X. Neither X nor R(X) can contain any leading zeroes.

* A Conference commenced on a given day precisely at 10*X/ 143 minutes past P o'clock ( but before P+1 o'clock) and concluded at 10*R(X) / 143 minutes past Q o'clock ( but before Q+1 o'clock) on the same day ; where 11 >=Q > P >=1 with the proviso that P and Q are whole numbers. It was observed that the hour hand and the minute hand had exchanged places during the respective times of commencement and conclusion of the said conference.

* Determine X, R(X), P and Q and,hence or otherwise, find the precise times of commencement and conclusion of the conference.

(In reply to re(2): computer solution-spoiler by Charlie)

Thanks Charlie.  I must have had some rounding error, or divided by 100 instead of 60 somewhere along the way.  I should have checked my work before posting, but when two of the 7 answers I came up with matched yours, I thought I was on to something.

Posted by MindRod on 2005-12-09 23:29:25