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Simple Train Journeys

Stage: 1 and 2 Challenge Level: Challenge Level:1

Well, here's a train route. The train starts at the top and makes a number of visits to the stations.
Now let's suppose that the train is going to make visits to three stations (they do not have to be different stations - each station can be visited several times!).
Journeys
So the first station would be Dorby - this will always be the case! (Why?)
Then the train can go on to Ender. When at Ender it could return and visit Dorby again OR it could go on to Floorin.
So two different journeys:
Dorby - Ender - Floorin
Dorby - Ender - Dorby

Your challenge is to find all the different journeys for visiting four stations.

You could then go on to find all the different journeys for visiting more stations - try five.
How about six stations?

Can you predict the number of different journeys for visiting seven stations? Were you right?

How would you predict the number of different journeys for visiting eight stations?

You might like to then invent your own routes that may go further than this one and then answer similar questions that you can think up.


The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities can be found here.
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NRICH is part of the family of activities in the Millennium Mathematics Project.