Trainspotting

A puzzle from James F. Fixx’s More Games for the Superintelligent, 1976:

A man who likes trains walks occasionally to a nearby railroad track and waits for one to go by. Afterward he notes whether he saw a passenger train or a freight. After several years his notes show that 90 percent of the trains he’s seen have been passenger trains. One day he meets an official of the railroad and is surprised to learn that the passenger and freight trains on this line are precisely equal in number. If the man timed his trips to the track at random, why did he see such a disproportionate number of passenger trains?

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All the trains run hourly, but the freight trains follow six minutes after the passenger trains. So if the man arrives at the track at random, his odds of arriving after a freight train and before a passenger train are 9 to 1; for 54 out of every 60 minutes, a passenger train will be the next to pass.

March 31, 2022March 30, 2022 | Puzzles