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MathNet 2024-part-03 — 168 problems (EN–VI) Question 102

Math Olympiad Vault · MathNet 2024-part-03 — 168 problems (EN–VI)

Question 102

In a hexagonal grid with unit side lengths, vertices are connected by paths of unit length. Two vertices are considered adjacent if they are connected directly by such a path.
Determine the minimum number of cities that can be placed on the vertices such that no two cities are placed on adjacent vertices, and no more cities can be added without violating this condition.

Question illustration

(Orgil-Erdene Erdenebaatar)