4

Part of 2015 Finnish National High School Mathematics Comp

Problems(1)

bw squares in nxn grid, coloring with limits on 2x2 square coloring

Source: Finland 2015, Problem 4

n

be a positive integer. Every square in a

n \times n

-square grid is either white or black. How many such colourings exist, if every

2 \times 2

-square consists of exactly two white and two black squares? The squares in the grid are identified as e.g. in a chessboard, so in general colourings obtained from each other by rotation are different.

square gridColoringcombinatorics