How to move knights so that black moves first? From move 0, what shortest-possible sequence of moves could be played so that the pieces are arranged exactly as standard board setup (with allowed swapping of same-color knights), but it is black's turn to move?  Is it even possible?
I thought about it and conjectured white would have to make an odd number of knight moves, and black would have to make an even number of knight moves. I think this is impossible when the knights need to end up where they started, or even swap with each other (because even though this is an odd number of moves for one knight, the other knight would also have to make an odd number of moves). Am I correct? How can it be proven?
I also guess that this is a famous or at least previously explored problem. Maybe it's trivial.
It's impossible. Knights require an even number of moves to reach a square of the same color as where they started, or correspondingly an odd number of moves to reach the opposite color. Both sides need to make an even number of moves to reach the starting position.