A Mathematical Problem?

Wooden toy train track

Wooden toy train track

The train track pictured uses almost all of our available pieces. The one piece not used is shown in the picture.

Not all parts of the track are reachable by the train in its current position. There is one tiny link towards the top that is not. If the train is turned to face the other way then all parts become reachable but only once.

Is it possible, using the pieces available to us, to construct a track for which from any starting position and direction it is possible for the train to traverse all of the track in either direction?

I’d imagine we’d have to make a big loop with a turning loop of some kind, or do we need two turning loops in opposite directions?

Solution

It’s really simple. Two turning loops one at each end. The most basic solution is a dog bone. Then to use up the remaining pieces just fill in between them. I’ll have to build it if James allows me and photograph it. James is starting to enjoy building his own tracks.

Solution to the train track problem

Solution to the train track problem

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