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: computer solution-spoiler
At 4:56:51, the hour hand would be at a position corresponding to (4+56/60+51/3600)*5 = 24.7375 minutes past the hour for the minute hand, which doesn't match the minute portion of 11:22:14.
For the others, I don't know your P and Q values, but for example, for 243 with 342, 4:16.99's hour hand position corresponds to 21.416 minutes past the hour and 5:16.99 corresponds to 26.416 minutes past the hour, when you actually need to match the 23.916 of 3:23.916.
Edited on December 9, 2005, 10:06 pm
Posted by Charlie
on 2005-12-09 21:54:58