@Rob_AOE said in #53:
> Either I'm not smart enough or its because of the language barrier, but I didn't quite get the logic of illegal mirrors / knights circling thing
What do you think is hard to follow?
The mirror image of the starting position is the same position with Black to move.
We claim this position is not legal, i.e. it cannot be reached in a game of chess.
The only attempt to achieve it is to move knights around and hopefully "lose a tempo" so that it becomes Black to move after you reach the starting array again.
This turns out to be impossible because of a parity problem.
In a nutshell, count +1 for every knight (either white or black) that lies on a dark square. Ignore knights on light squares. The starting position has a count of +2. If you move, 1. Nc3 the count goes up to +3 and if you then answer with 1... Nf6 the counts increases again to +4. The thing is that when it is White to move, the counter is even and when it is Black to move, the counter is odd. This means that it will always be White to move when you reach the starting array.