MathDB

Problem 6

Part of 1991 Bulgaria National Olympiad

Problems(1)

putting white/black checkers on nxn board

Source: Bulgaria 1991 P6

6/3/2021
White and black checkers are put on the squares of an n×nn\times n chessboard (n≥2)(n\ge2) 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.
combinatoricsgame