My father came up with a puzzle and dared me to solve it. I could solve it by trial and error, but I rather want to solve it mathematically. It is the so called "Wedding Vows puzzle" where you have to get the two seperated rings together on one side.
But the problem is: I don't know how to start. I thought about interpreting the little piece of wood as a compact surface of genus $2$ by identifying the left hole with the right hole. Then I could think about the rope as a path on the surface. But how could I proceed?
Does anybody know how to solve it?