putting white/black checkers on nxn board
Source: Bulgaria 1991 P6
June 3, 2021
combinatoricsgame
Problem Statement
White and black checkers are put on the squares of an chessboard according to the following rule. Initially, a black checker is put on an arbitrary square. In every consequent step, a white checker is put on a free square, whereby all checkers on the squares neighboring by side are replaced by checkers of the opposite colors. This process is continued until there is a checker on every square. Prove that in the final configuration there is at least one black checker.