...and consequently got me thinking.
Starting anywhere you want, travel on a continuous path and go through every station on the map.
What is the least number of stations you will have to pass through more than once?
If this is too hard to read, you can probably Google your own
So, I think I have a solution but I'm not going to tell anyone.
You have to think for yourself.
To extend this idea, you could:
1. Choose a mandatory starting point, such as Changi Airport or Dhoby Ghaut.
2. Say you can only travel on the red and yellow lines in a clock-wise direction.
3. Use the maps for other underground railway networks, like London, Paris, New York, Tokyo....or anywhere you want!