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: Sanity check (spoiler)=rectification by Ady TZIDON)

I think we all agree that this depends on interpretation, which is why I offered different levels of numbers in the solution. It's conceivable to take the hint from the puzzle, "Including trains seen at the starting point and the ones they are traveling on" to imply that a train seen at the ending point is not to be counted: after all, why mention the starting point but not the ending point? But that's also why I included also the possibility of including the ending point.

But your statement "A fence of 20 segments needs 21 posts." is not true of a circular fence, which is what gets us into this confusion.

It would have been better if KS had specifically addressed the ending point of the trip, but he did not. Also unadressed was whether physical trains or merely train encounters were being counted, which I also adressed in my solution, with smaller numbers counting each physical train only once no matter how often it was met.

Posted by Charlie on 2013-07-13 10:06:37