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Saudi Arabia 2024 counting and probability
Problem
A rhombus of side length 1 and internal angle 60° is called a diamond. Suppose that a regular hexagon of side length is dissected into diamonds. Prove that each main diagonal of the hexagon halves exactly diamonds.
Solution
Divide the hexagon into triangular cells (in each dissection every diamond will consist of two of them) and consider a half of the hexagon (on one side on a fixed main diagonal ).
Techniques
Coloring schemes, extremal argumentsInvariants / monovariantsCounting two waysCombinatorial Geometry