2500 chess kings have to be placed on a chessboard
Source: IMO Shortlist 2010, Combinatorics 3
July 17, 2011
matrixcombinatoricsChessboardcountingIMO Shortlist
Problem Statement
2500 chess kings have to be placed on a 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.)Proposed by Sergei Berlov, Russia