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ASU 049 All Russian MO 1964 9.5 shortest path in hexagon

Source:

June 18, 2019
minimumhexagongeometry

Problem Statement

A honeybug crawls along the honeycombs with the unite length of their hexagons. He has moved from the node AA to the node BB along the shortest possible trajectory. Prove that the half of his way he moved in one direction.