Is it possible to position all chess pieces on the board such that all pieces defend at least one piece and attack at least one piece?
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When you say "pieces," do you mean just the pieces, or the pawns as well?– BlueRaja - Danny PflughoeftCommented May 8, 2011 at 16:25
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I mean the pawns as well. I think doing it that way makes it more interesting and complicated... :P– El'endia StarmanCommented May 8, 2011 at 17:40
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This reminds me of a computer problem, How do place X (I forgot the number) queens on the board so they don't "attack" each other?– Tom AuCommented Jun 9, 2011 at 20:59
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@Tom: Perhaps you're thinking of this one? math.utah.edu/~alfeld/queens/queens.html– El'endia StarmanCommented Jun 9, 2011 at 21:20
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@El'endia: Exactly.– Tom AuCommented Jun 9, 2011 at 21:22
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2 Answers
Yes, and it's not particularly hard to do. Here's one solution.
I found this by placing the pawns first (because they are much more limited in their attack/defence potential), and then adding the pieces one at a time. Using this simple manual approach, it took about 15 minutes to find a solution. As an added constraint, I avoided placing the kings in check.
There are undoubtedly many alternative arrangements that would also work. It would be quite straightforward to write a computer program to search for valid configurations. A simple brute-force backtracking algorithm would probably suffice.
answered May 9, 2011 at 2:35
It cannot be done "naturally" in a normal chess game though.
The pawns on columns A and H only have 1 square of influence for attacking/defending, since they are on the edge of the board. To move them further into the board, they would have to capture another piece, and if you do, you don't have all the pieces on the board anymore.
