2010 IMO Shortlist C3

2500 chess kings have to be placed on a $100 \times 100$ chessboard so that (i) no king can capture any other one (i.e. no two kings are placed in two squares sharing a common vertex); (ii) 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.) (Russia) Answer. There are two such arrangements.

必须将 2500 个国际象棋国王放置在 $100 × 100$ 的棋盘上，以便 (i) 没有国王可以捕获任何其他国王(即没有两个国王被放置在共享公共顶点的两个方格中)； (ii) 每行每列恰好包含 25 个国王。求这种排列的数量。 (旋转或对称性不同的两种排列应该是不同的。)(俄罗斯)答案。这样的安排有两种。