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 computer solution-spoiler by Charlie)

or the late evening meeting 6:47:50 to 9:33:59.

I found other answers, Charlie.  Would you mind reviewing my solution and pointing out why my values don't work?

Posted by MindRod on 2005-12-09 21:23:42