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Is it possible to setup a chess board where every square on the board is only controlled once. Occupying a square does not mean controlling it.

If it is possible, with how little pieces?

Piece Cost:

  • Pawn: 1

  • Bishop: 3

  • Knight: 3

  • Rook: 5

  • Queen: 9

You are not allowed to use the king.

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  • $\begingroup$ Related meta question: meta.puzzling.stackexchange.com/questions/1321/… $\endgroup$ Commented Oct 20, 2014 at 14:39
  • $\begingroup$ "Once and only once", or "at least once"? $\endgroup$ Commented Jan 30, 2016 at 5:14
  • $\begingroup$ Once and only once, "only controlled once". $\endgroup$ Commented Mar 20, 2017 at 8:42

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I found it very hard to only control each square once. Any attempt at limiting the physical number of pieces was turning into an issue. I suspect this can be beaten, but I can manage the whole board in 32 pawns. At least they're only 1 point each.

32.

32 Points

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  • $\begingroup$ :) This time it wasnt explicit that they have to be of the same colour, so yeah this is good and I dont think this can be beaten, at least not easily $\endgroup$ Commented Oct 18, 2014 at 4:28
  • $\begingroup$ @skv would it have mattered if they were all white? Each square would still only be controlled once. $\endgroup$ Commented Oct 18, 2014 at 11:44
  • $\begingroup$ @Joel Great work! I wonder if it's possible without it all being 32 pawns... Can 32 be beaten? $\endgroup$ Commented Oct 18, 2014 at 11:45
  • $\begingroup$ @skv wait I see it now, so yea both colours are allowed. $\endgroup$ Commented Oct 18, 2014 at 11:51
  • $\begingroup$ puzzling.stackexchange.com/questions/3006/… $\endgroup$ Commented Oct 18, 2014 at 11:53

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