The article isn't very accurate. In the episode, two people can swap minds, but the same two minds cannot be swapped twice. The article says that "after enough

The article isn't very accurate. In the episode, two people can swap minds, but the same two minds cannot be swapped twice. The article says that "after enough swaps everyone can find their original body." But this is incorrect. The actual math problem solved says that by adding two people to the pool (the harlem globetrotters in the episode) you can then always find a way for everyone to swap into their original bodies. The math proof shows this by starting with an arbitrary permutation of minds (pi) for n people, then adds two new people x and y to show that there now exists another permutation of minds (sigma) that "undoes" the original permutation. This means there's a way for everyone to get their bodies back. Without the addition of two people x and y there is no such guarantee. To understand the details you'll need to know about group theory. Specifically permutations. This isn't a "deep" problem. But it is awesome that it's correct and on TV!