Check out Gary Bene’s gbUnSnarl game. Your job is to drag the nodes in a network to unsnarl it.
Basically it asks you to find a way to rearrange a planar network so none of its edges intersect. Algorithms to prove that a network is planar are fairly complicated. The networks generated by the game are guaranteed to be planar, so there are always solutions. The only question is, “Can you find them?”