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A 2005 x 2005 board

Source:

November 23, 2011
combinatorics unsolvedcombinatoricsSweden

Problem Statement

Every cell of a 2005×20052005 \times 2005 square board is colored white or black so that every 2×22 \times 2 subsquare contains an odd number of black cells. Show that among the corner cells there is an even number of black ones. How many ways are there to color the board in this manner?
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