Page 1 of 1

2010 C3

Posted: Mon Aug 08, 2016 1:31 am
by Kazi_Zareer
$2500$ 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.)