Competition problem — Combinatorics

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Combinatorics Difficulty 5.6 AIME, harder Prove it Belarus

2500 chess kings have to be placed on a $100 \times 100$ chessboard so that
1) no king can capture any other one (i.e. no two kings are placed in two squares sharing a common vertex);
2) 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.)
(IMO-2010 Shortlist, Problem C3)

Solution

3. See IMO-2010 Shortlist, Problem C3.

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