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Using one color, White or Black, place as many chess pieces (kings, queens, bishops, knights, rooks, and pawns, or combinations thereof) as you can on a checkerboard so that when the number of pieces is multiplied by the number of the possible moves, we get the greatest value S , where S = (no.of pieces) X (no. of moves). Without having the pieces attacking each other, what is the greatest value possible?

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  • $\begingroup$ Does "without attacking" mean "without threatening" (which would limit the number of pieces) or do just mean without counting attacking moves? $\endgroup$ – Daniel Mathias Mar 21 at 0:30
  • $\begingroup$ @Daniel Mathias-It seems that my answer to your comment on had never added. That is, without attacking or capturing or threatening of other pieces . Thus Qs cannot be side by side $\endgroup$ – TSLF Mar 21 at 6:56
  • $\begingroup$ Answer updated accordingly. $\endgroup$ – Daniel Mathias Mar 21 at 11:30
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32 knights and the number of possible moves for each:
 N . N . N . N .   2 . 4 . 4 . 3 .  =13
 . N . N . N . N   . 4 . 6 . 6 . 3  +19=32
 N . N . N . N .   4 . 8 . 8 . 6 .  +26=58
 . N . N . N . N   . 6 . 8 . 8 . 4  +26=84
 N . N . N . N .   4 . 8 . 8 . 6 .  +26=110
 . N . N . N . N   . 6 . 8 . 8 . 4  +26=136
 N . N . N . N .   3 . 6 . 6 . 4 .  +19=155
 . N . N . N . N   . 3 . 4 . 4 . 2  +13=168
 32*168=5376

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