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Every 3x3 square of an nxn board has such a colouring

Source: Pan African MO 2013 Q5

June 30, 2013
symmetrycombinatorics unsolvedcombinatorics

Problem Statement

The cells of an n×nn\times n board with n≥5n\ge 5 are coloured black or white so that no three adjacent squares in a row, column or diagonal are the same colour. Show that for any 3×33\times 3 square within the board, two of its corner squares are coloured black and two are coloured white.
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