2010 C3
Posted: Mon Aug 08, 2016 1:31 am
$2500$ 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.)
(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.)