Two travelers set out at the same time to travel opposite ways round a circular railway. Trains start each way every fifteen minutes: on the hour, fifteen minutes past, half past, and forty-five minutes past. Clockwise trains take two hours for the journey, counterclockwise trains take three hours.

Including trains seen at the starting point and the ones they are traveling on, how many trains did each traveler see on his journey?

(In reply to re: solution by Ady TZIDON)

The relevant paragraph in my original post, to which I've now added emphasis:

Between the time the clockwise train sets out and the time it returns to its starting station, someone on it will see all the trains currently on the other track (that's 12) plus all those that set out during that 2-hour interval, which is 8, making 20. Of course he also sees his own train, bringing the total up to 21, but we could also say that he sees the train of the other traveler in the question twice, making 22 in all.

I did it in this piecemeal manner as the puzzle mentioned the starting point but not the ending point. But I did feel it sufficiently compelling to think the ending point was as important as the starting point.

Posted by Charlie on 2013-07-12 22:17:17