King of Kings

Discrete Mathematics Level pending

2500 chess kings have to be placed on a \(100 \times 100\) chessboard so that

  • no king can capture any other one (i.e. no two kings are placed in two squares sharing a common vertex);

  • each row and each column contains exactly 25 kings

Find the number of such arrangements. (Two arrangements differing by rotation or symmetry are supposed to be different.)

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