7. Bronx vs. Brooklyn

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A YOUNG MAN lives in Manhattan near a subway express station. He has two girl
friends, one in Brooklyn, one in The Bronx. To visit the girl in Brooklyn he
takes a train on the downtown side of the platform; to visit the girl in The Bronx
he takes a train on the uptown side of the same platform. Since he likes both
girls equally well, he simply takes the first train that comes along. In this way he
lets chance determine whether he rides to The Bronx or to Brooklyn. The young
man reaches the subway platform at a random moment each Saturday afternoon.
Brooklyn and Bronx trains arrive at the station equally often—every 10 minutes.
Yet for some obscure reason he finds himself spending most of his time with the
girl in Brooklyn: in fact on the average he goes there nine times out of ten. Can
you think of a good reason why the odds so heavily favor Brooklyn?

The answer

The answer to this puzzle is a simple matter of train schedules. While the
Brooklyn and Bronx trains arrive equally often—at 10-minute intervals—it
happens that their schedules are such that the Bronx train always comes to this
platform one minute after the Brooklyn train. Thus the Bronx train will be the
first to arrive only if the young man happens to come to the subway platform
during this one-minute interval. If he enters the station at any other time—i.e.,
during a nine-minute interval—the Brooklyn train will come first. Since the
young man’s arrival is random, the odds are nine to one for Brooklyn.
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