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.)

The answer is 2.

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This is a 2010 IMO problem. The full solution is here .