Planarity.net is a nifty game I found on LifeHacker tonight. You just shift around network nodes until the lines are all uncrossed. The good news is that you can easily play it over and over and over. I’ll let you guess the bad news. Like Sudoku puzzles, it’s a breeze to teach a computer how to solve it, but for some reason it particularly tickles our mushy wet-brains. As you play with it, you start to get an idea how an untangling algorithm would work.
If you have any obsessive-compulsive tendencies, please don’t follow this link (on the other hand, you’ll quite enjoy it). This game is so simple, mindless, and pleasing in that clean-it-up-and-make-it-better way that it could practically be used as a diagnostic tool.