(a) An infinite sheet is divided into squares by two sets of parallel lines. Two players play the following game: the first player chooses a square and colours it red, the second player chooses a non-coloured square and colours it blue, the first player chooses a non-coloured square and colours it red, the second player chooses a non-coloured square and colours it blue, and so on. The goal of the first player is to colour four squares whose vertices form a square with sides parallel to the lines of the two parallel sets. The goal of the second player is to prevent him. Can the first player win?(b) What is the answer to this question if the second player is permitted to colour two squares at once?(DG Azov)PS. (a) for Juniors, (a),(b) for Seniors
gamegame strategyinfinite boardColoringcombinatoricscombinatorial geometry