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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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-1 Irrelevant to play. –  aramis May 8 '11 at 7:25
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+1 interesting question for all chess fans and good tactical exercise! –  user545 May 8 '11 at 13:03
    
When you say "pieces," do you mean just the pieces, or the pawns as well? –  BlueRaja - Danny Pflughoeft May 8 '11 at 16:25
    
I mean the pawns as well. I think doing it that way makes it more interesting and complicated... :P –  El'endia Starman May 8 '11 at 17:40
    
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 Au Jun 9 '11 at 20:59

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up vote 18 down vote accepted

Yes, and it's not particularly hard to do. Here's one solution.

enter image description here

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.

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+1. But I'd move the R on e8 to c8 instead. On e8 it's not really "defending" anything, since the K can't be "defended" (defending is preventing something from being taken because of retaliation, which of course doesn't apply to the K). But then the black K isn't defending anything, so move it to e7 instead. (Did I miss something?) –  msh210 Jan 18 '12 at 19:06
    
@msh210 - On c8, the black rook wouldn't be attacking anything, so I don't think that's a valid solution. Regarding defense of the king, I agree, but bear in mind this whole position is already very artificial (although I tried to make the pawn positions vaguely real-looking). –  ire_and_curses Jan 18 '12 at 19:29
    
Hm, so maybe put the R on e7 instead of e8. –  msh210 Jan 18 '12 at 19:31
    
Yes, that would work. @Dave DuPlantis - do you think you could redo the image to move the black rook on e8 to e7 (I'm not sure how you generated it in the first place)? –  ire_and_curses Jan 18 '12 at 19:36
    
@ire, I used this page, the one I linked to in the chess tag wiki. If there are similar sites, we might want to update the wiki or perhaps find a more visible spot for them? –  Dave DuPlantis Jan 18 '12 at 22:04

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