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SE-SKOLORNAS 2013 Problem 4

    A robotic lawnmower is located in the middle of a large lawn. Due a manufacturing defect, the robot can only move straight ahead and turn in directions that are multiples of 60o60^o . A fence must be set up so that it delimits the entire part of the lawn that the robot can get to, by traveling along a curve with length no more than 1010 meters from its starting position, given that it is facing north when it starts. How long must the fence be?

    Dataset text AI-MO AoPS. Quoted with source.

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