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Costa Rican math olympiad 2008 Problem 1

Source:

June 18, 2009
combinatorics unsolvedcombinatorics

Problem Statement

We want to colour all the squares of an nxn nxn board of red or black. The colorations should be such that any subsquare of 2x2 2x2 of the board have exactly two squares of each color. If n≥2 n\geq 2 how many such colorations are possible?
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