# Move chess pieces to flip starting position in center

The white pieces in the above position should maneuver themselves into the flipped starting position (i.e. king in e3). All pieces makes regular moves within the 4x4 center squares. By removing a pawn from the board to allow a moving space, find a way with least moves.

• The starting position has a removed pawn thus its symmetry. removing not considered a move.
– TSLF
Sep 3, 2020 at 21:08
• What I do first is to calculate the number of status of the board, which (with one pawn removed) is at most $16! / (7! 2!2!2!) = 518918400$. It should be even less, because pawns only move forward. Thus it is perfectly bruteforceable (: Sep 3, 2020 at 23:50
• @WhatsUp- It is also perfectly learnable. 1) side pawns are not removable 2) pawns makes 14 or 15 moves only.
– TSLF
Sep 4, 2020 at 5:27
• Just verifying - e6 goes to e3?
– Moti
Sep 5, 2020 at 18:49
• @Moti- yes, the only possible flip
– TSLF
Sep 6, 2020 at 16:08