Mr. Tsuru commutes each day by train between his home and the downtown office building where he works. Trains run back and forth on the line from the brown station at one end to the purple station at the other end. There are dozens of stations. We’ve shown only five of them. Mr. Tsuru works near the blue station. His home is halfway between the red and yellow stations, so he can use either to get home in the same time.

Trains constantly come through the blue station in both directions. So, when he leaves work, Mr. Tsuru can take the train in either direction. His approach is to take the train that arrives first regardless of the direction it is traveling. If it is going one way he will end up at the red station. If it is going the other way he will arrive at the yellow station.

In each direction, the trains are spaced exactly 10 minutes apart. Mr. Tsuru works very irregular hours, so the time he leaves work varies greatly and the time at which he reaches the blue station is essentially random.

He expects that he will be going home via the red station about half the time and via the yellow station the other half. But, after several months of commuting he finds that he is using the red station about 90% of the time. How is this possible?

Try your luck, then check our solution.

This puzzle was suggested by Martin Gardner in his book “My Best Mathematical and Logic Puzzles”