# Brainteaser #15- Love Train -

A young man, living in Manhattan, New York, has two girlfriends. One lives to the North, in the Bronx, and
the other lives to the South, in Brooklyn.

He likes both girls equally but can only visit one each weekend. He therefore leaves it to chance and
takes the first train that arrives when he reaches the train station.

Even though the man arrives at a totally random time every Saturday morning and the Brooklyn and Bronx
trains arrive equally often (every ten minutes), he finds himself visiting the girl in Brooklyn on average
nine times out of ten. How could the odds so heavily favor taking the Brooklyn train?

**HINT**: Think of a way the train schedules might favor one train over the other.

**ANSWER**:

*The Brooklyn train leaves exactly 1 minute before the Bronx train.*
**EXPLANATION**: Let's say the Brooklyn train arrives at 09:00, 09:10, 09:20, etc. and the Bronx train
arrives one minute after at 09:01, 09:11, 09:21, etc. Consider the ten minute interval from 09:00 to
09:10. If the man arrives between 09:00 and 09:01, the 09:01 Bronx train will be the first to arrive
(assuming that he doesn't arrive at exactly 09:00). If the man arrives between 09:01 and 09:10, the 09:10
Brooklyn train will be the first to arrive. In any ten minute period, the Brooklyn train will be the first
to arrive in nine of the ten minutes.

Do you have a

suggestion for this puzzle (e.g. something that should
be mentioned/clarified in the question or solution, bug, typo, etc.)?