Tashy and Lynn sent us diagrams to help explain how they went about tackling this problem:

For the first track, we just worked out how to do it by looking at the track. In our diagram, Tashy went from station 3 to station 4 to station 1 to station 3 to station 2 to station 1 and Lynn went from station 3 to station 1 to station 2 to station 3 to station 4 to station 1.

Railway 1


We noticed that we went through stations 1 and 3 twice but stations 2 and 4 only once. We think this is because there are three tracks coming out of stations 1 and 3 so if we only went through the station once we'd only go on two tracks, but we need to come back again to go on the third track.

For the second track we could start anywhere and go anywhere and as long as we didn't double back on ourselves we got all the way round. We think this is because there are only two tracks coming out of each station, so you don't have a choice - you go in one and out one.

For the third track we split the track up into two different tracks. There is the square, with stations 1, 2, 3 and 4 as corners, and the two diamonds. We went along one and then went along the other. We started at station 1 on our diagram and then went 1-2-6-3-4-5-1, which were the two diamonds, and then went 1-4-2-3-1, which was the square.
Railway 3
For the fourth track we had to start at 1 or 4, because they had three tracks and so had to be visited more than once. We went 1-3-2-4-1-5-1 in our diagram.
Railway 4
We could not do the fifth track. We think this is because all the stations had three tracks going into them, and so you could go out-in-out of the one you started at and then in-out-in another, but then you were stuck in the second station and had only gone on five of the six tracks.
We split the last track up into two, like we did with the third one. There was the square with corners 1, 2, 3, 4 and the other track. The other track had two corners with three tracks so we had to start at one and end at the other. We started at 2 and went 2-6-3-4-7-2-1-5-4, and then we did the square 4-2-3-1.
Railway 6
Thank you very much, Tashy and Lynn!