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enter image description here

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?

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    $\begingroup$ 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. $\endgroup$
    – bobble
    Feb 15, 2022 at 23:52
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    $\begingroup$ Is castling and/or pawn promotion valid moves? $\endgroup$ Feb 16, 2022 at 1:31
  • $\begingroup$ @bobble -yes separate , for these are the max & min $\endgroup$
    – TSLF
    Feb 16, 2022 at 3:40
  • $\begingroup$ @risky mysteries-yes valid moves as regular moves $\endgroup$
    – TSLF
    Feb 16, 2022 at 3:42
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    $\begingroup$ Thank you, I've been trying to solve a different problem. $\endgroup$ Feb 16, 2022 at 18:21

1 Answer 1

5
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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:

enter image description here

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

enter image description here

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:

enter image description here

Alternative without promotion (8m/8r):

enter image description here

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:

enter image description here

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    $\begingroup$ 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. $\endgroup$
    – TSLF
    Feb 16, 2022 at 17:38
  • $\begingroup$ 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. $\endgroup$
    – TSLF
    Feb 17, 2022 at 3:16
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    $\begingroup$ @TSLF Wait, so there is also a no-promotion solution? If so, I'll look for it :) $\endgroup$ Feb 17, 2022 at 4:03
  • $\begingroup$ @risky mysteries-Actually, you can.. $\endgroup$
    – TSLF
    Feb 17, 2022 at 4:10
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    $\begingroup$ Thank! I can't believe I have been fiddling around with 2 bishops for so long when I should've removed one of those! $\endgroup$ Feb 19, 2022 at 15:15

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