Problem #PRU-5132

Problems Mathematical logic Invariants

Problem

All the squares of a \(9 \times 9\) chessboard were coloured black and white in a traditional way, such that the corner squares are all white. With each move you can choose two neighbouring squares and change both of their colours - black to white and white to black. Can you reach a chessboard that is all black in this way? (Squares that are one diagonal away also count as being neighbors)