This weekend I was helping my three year old build some train tracks for his Duplo train. The train is powered by a small battery, so it moves on its own. His collection of pieces includes a bunch of straights and turns, and two switches. This is what we built:
The train can approach a switch from three possible directions:
When the train comes from direction 1, it will follow the path that is opened by the red lever on the switch. When the train comes from one of the other two directions, there is only one way to go. If the switch is in the way, it will be pushed aside by the train (direction 3 in the example).
I want to build a track where the train continuously loops across the entire track system, moving switches as needed. I want to know the minimum number of pieces required to achieve this. Some restrictions:
- The solution has to work for each starting point and each traveling direction.
- The solution has to include more than two switches.
- No human interaction is allowed other than initial placement and activation of the train.
All I managed to find is a solution with two switches and 24 curves, similar to the one that @JonTheMon used for his answer. I want to know if there's a solution when using more than two switches.