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2 colour game in a 8x8 chessboard, B can always prevent A from winning

Source: Dutch NMO 2006 p5

September 21, 2019
winning strategycombinatoricsChessboardColoring

Problem Statement

Player AA and player BB play the next game on an 88 by 88 square chessboard. They in turn color a field that is not yet colored. One player uses red and the other blue. Player AA starts. The winner is the first person to color the four squares of a square of 22 by 22 squares with his color somewhere on the board. Prove that player BB can always prevent player AA from winning.
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