Cevap 36. Mathematica ile cozumu:
n = 4;
MatrixForm[mat = Array[a, {n, n}]];
loc = Join @@ Table[{i, j}, {i, n}, {j, n}];
nf = Nearest[Tuples@Range@Dimensions@mat -> Flatten@mat];
fourNeighbors[pt_] := nf[pt, {All, 1}][[2 ;; All]]
cond = Thread[Total /@ fourNeighbors /@ loc == 6];
var = Flatten@mat;
obj = Total@var;
sol = Maximize[{obj, cond}, var];
Partition[var /. Last@sol, n] // MatrixForm
4x4chess.pdf (62 kb)
Birkac gozlem: Min yapan matrixle Max yapan matrix aynidir. Simetrik olan sayilarin yeri degisebilir.
n tek ise cozum yok gibi..
n=4
(6006600600000660)
n=6
(006660600−6006060660−66000606000600066)
n=8
(6006600660000006006006000060060060000006600660060000000006600660)
n=10
(600066066−6606000−60600−66006600660600060−6660006−6060600001200600066−600000000600660666−606000−60012006006660)
n=12
(6060060660066−66006−6000066−6600606060060600006−660000006006−66060600600606−660600000006−660006066006066006−60000000600606066060000006−600−660066006066060)
Download the PDF: 4x4chess.pdf