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 60o. 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 10 meters from its starting position, given that it is facing north when it starts. How long must the fence be? geometrycombinatoricscombinatorial geometry