Rainbow Tangle

Rainbow Tangle is a game on a sequence of permutations. The purpose of the game is to create as straight routes of the permutation particles as possible.

The game can be installed on a Windows Phone 7 from here.

When playing this game the player tries to find a tangle which we, that is Alexander Holroyd, Sergey Bereg, Sergey Pupyrev, and Lev Nachmanson, started calling a nice tangle. We know something about these tangles, but we don't have a polynomial time algorithm deciding if a permutation can be solved by a nice tangle. In other words, we cannot solve a game automatically in real time on a phone. We wrote a paper on nice tangles explaining the mathematics behind the game.