# Move and Remove

From the initial position Black makes a regular move to an unoccupied square, and removes any piece from the board. Then repeats, alternately making a move and a removal. The objective is for Black to find a position where all the unoccupied squares are under attack.

a) How can Black make it with ten moves?

b) With only eight removed pieces?

• Are the "ten moves" and "eight removed pieces" separate sub-questions? I don't see how they're compatible - if you've made ten moves, you've removed more than eight pieces. Feb 15, 2022 at 23:52
• Is castling and/or pawn promotion valid moves? Feb 16, 2022 at 1:31
• @bobble -yes separate , for these are the max & min
– TSLF
Feb 16, 2022 at 3:40
• @risky mysteries-yes valid moves as regular moves
– TSLF
Feb 16, 2022 at 3:42
• Thank you, I've been trying to solve a different problem. Feb 16, 2022 at 18:21

Part 1: 10-mover

1.e7-e5 xa7 2.e5-e4 xb7 3.e4-e3 xc7 4.e3-e2 xd7 5. e2-e1Q xf7 6.Qd8-d5 xg7 7.Bf8-d6 xh7 8.Bd6-c7 xb8 9.Ra8-a2 xg8 10.Ke8-f7

Final position:

Alternative with no promotion (final position only; reachable in 10 moves / 9 removals):

Part 2: 8-remover

1.g7-g5 xa7 2.g5-g4 xb7 3.g4-g3 xc7 4.g3-g2 xd7 5.g2-g1Q xe7 6.Qd8-d3 xf7 7.Bf8-g7 xh7 8.Bg7-e5 xg8 9.Nb8-c6

Final position:

Alternative without promotion (8m/8r):

Aside: if we aim for a fast solution it can be done in

5 moves and 4 removals (3 if strict alternating is not required.

Proof game:

1.e7-e5 xh7 2.Rh8-h2 xd7 3.Qd8-d6 xa7 4.Ra8-a1 (xb7) 5.Bf8-e7

Final position:

• Good one! This is an early solution for all free squares attacked in just 9 ply or 5 moves. But onward to next removal..xf7 ,and move 6.Ke8-f7 makes it further. The problem is how to reach 10th move while losing more pieces.
– TSLF
Feb 16, 2022 at 17:38
• Right.10 moves is the upper limit and the 9 mover hints for solving the least moves. I didnt find a promotion solution so allowed it. I guess the solution for no promotion is unique.
– TSLF
Feb 17, 2022 at 3:16
• @TSLF Wait, so there is also a no-promotion solution? If so, I'll look for it :) Feb 17, 2022 at 4:03
• @risky mysteries-Actually, you can..
– TSLF
Feb 17, 2022 at 4:10
• Thank! I can't believe I have been fiddling around with 2 bishops for so long when I should've removed one of those! Feb 19, 2022 at 15:15