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MEMO 2010, Problem T-4: Coloring vertices

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September 12, 2010
combinatorics proposedcombinatorics

Problem Statement

Let nn be a positive integer. A square ABCDABCD is partitioned into n2n^2 unit squares. Each of them is divided into two triangles by the diagonal parallel to BDBD. Some of the vertices of the unit squares are colored red in such a way that each of these 2n22n^2 triangles contains at least one red vertex. Find the least number of red vertices.
(4th Middle European Mathematical Olympiad, Team Competition, Problem 4)
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