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Least possible number of black triangles

Source: Baltic Way 2010

November 19, 2010
ceiling functioninductioncombinatorics proposedcombinatorics

Problem Statement

Let nn be an integer with n≥3n\ge 3. Consider all dissections of a convex nn-gon into triangles by n−3n-3 non-intersecting diagonals, and all colourings of the triangles with black and white so that triangles with a common side are always of a different colour. Find the least possible number of black triangles.
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