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red or blue edges in a square nxn lattice

Source: Ukraine TST 2018 p4

April 29, 2020
Coloringcombinatorics

Problem Statement

Let nn be an odd integer. Consider a square lattice of size n×nn \times n, consisting of n2n^2 unit squares and 2n(n+1)2n(n +1) edges. All edges are painted in red or blue so that the number of red edges does not exceed n2n^2. Prove that there is a cell that has at least three blue edges.
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