# Crazy Train

A man who lives in Middletown has two girlfriends, one in Northtown and one in Southtown. Trains from the Middletown train station leave for Northtown once every hour. Separate trains from the station also leave for Southtown once every hour. No trains go to both Northtown and Southtown.

Each day he gets to the Middletown train station at a completely random time and gets onto the first train that is going to either Northtown or Southtown, whichever comes first.

After a few months, he realizes that he spends 80% of his days with his girlfriend from Northtown, and only 20% of his days with his girlfriend from Southtown.

How could this be?

### 2 guesses to Crazy Train

• Nanao Ise

I believe that the trains for Northtown and Southtown leave twelve minutes apart, deduced by the fact that 80% of 60 is 48 and 20% of 60 is 12.

So say that the train for Northtown leaves every hour, and the train for Southtown leaves at every twelve past.

And for the sake of an example, let’s operate between a 1:00 and 2:00 time period. So if the man arrives at any time between 1:00 and 1:12, he will catch the Southtown train. And if he arrives at any time between 1:12 and 2:00, he will catch the Northtown train.

The likelihood of his coming in the 48-minute time gap given in taking the Northtown train is far higher than his coming in the 12-minute opening for the Southtown train, and so he spends more time with his girlfriend in Northtown.

Although he should probably stop dating one soon, and just spend 100% of his time with just one of them.

• Dude

Exactly correct, Nanao Ise.

You are today’s winner.