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 MathiasMar 21, 2020 at 0:30
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$\begingroup$ @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 $\endgroup$– TSLFMar 21, 2020 at 6:56
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$\begingroup$ Answer updated accordingly. $\endgroup$– Daniel MathiasMar 21, 2020 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
answered Mar 21, 2020 at 2:29