How should Black move as to attack all the squares that have no piece on them with only ten legal moves for black? Any unoccupied squares must be attacked. Start from the position above as shown.
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$\begingroup$ To clarify, squares that the black pieces are on do not need to be attacked? $\endgroup$– bobbleCommented Jan 19, 2021 at 18:09
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$\begingroup$ yes just all the squares without a piece $\endgroup$– TSLFCommented Jan 19, 2021 at 18:17
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$\begingroup$ requires well coordinated attack $\endgroup$– TSLFCommented Jan 21, 2021 at 3:03
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$\begingroup$ Rather annoyingly I can get this down to a single unattacked square which is just in front of a pawn. This is a good puzzle. $\endgroup$– hexominoCommented Jan 21, 2021 at 16:29
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$\begingroup$ one way or the other that works $\endgroup$– TSLFCommented Jan 21, 2021 at 17:09
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2 Answers
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Here are the moves:
With OP confirming we can either move up or down the board it can actually be done in 9:
[FEN "8/8/8/8/8/8/pppppppp/rnbqkbnr w kq - 0 1"] 1. null Na3 2. null b1=Q 3. null Bb2 4. null c1=Q 5. null Qb3 6. null d1=Q 7. null Qd8 8. null Qh7 9. null Qcc4
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Although Paul Panzer has given the correct solution, I thought it was worth adding another answer because
Even if you assume that black must play up the board you can get very very close (to the point that I'm still not sure if it is impossible).
Moves
[FEN "rnbqkbnr/pppppppp/8/8/8/8/8/8 w kq - 0 1"] 1. null d5 2. null d4 3. null d3 4. null d2 5. null d1=Q 6. null Q8d2 7. null h5 8. null h4 9. null b5 10. null e5
Replay
Notice here that the only unattacked square is e4 (in front of the pawn) which still seems "half" attacked given it is the only place the pawn can move next.
Also, it is possible to cover this square in one move
11. null Nf6
but you can see that this is close enough that it feels like a different line of attack could make it possible.
answered Jan 22, 2021 at 10:26
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$\begingroup$ Uh oh, this feels to me like that the question might be quite interesting if black can only play up the board. $\endgroup$ Commented Jan 22, 2021 at 11:42
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1$\begingroup$ FYI I added two more almost solutions to your CW over at chess meta. $\endgroup$ Commented Jan 22, 2021 at 14:33