# Zurich tram service problem

11 May 2004
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Mathematics

This is a little thought problem I learned during the Quantum Mechanics course I'm taking. It was (supposedly) A Einstein who thought about it first when he was working in Zurich.

As we all know, the tram service in Zurich runs like clockwork; all day every day. Or at least, let's assume so. This question appeared on one of my exercise sheets:

There is a tram service in the city of Zurich between two terminals A and B such that a tram (there is only one tram in service) leaves every five minutes from the terminals and makes the journey from A to B (B to A) in exactly five minutes. There is a passenger who comes to a stop C located 1/4 of the distance AB from A atcompletely randomtimes. He takes always the first tram regardless of the direction in which it arrives. He keeps all his tickets and after a year he counts how many times he travelled in the directions AB and BA. Explain why he finds that he travelled many more times in one direction than the other. What is the ratio of the number of journeys from A to B to the number of journeys from B to A?

If you can't be asked to do the simple calculation, at least figure out which direction he travelled more than the other. It's not a hard problem to understand so anybody can do it without any math skills. It's just a little mind boggling at first.

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