Home > Geometry, Problem Solving > Build a house in the forest

Build a house in the forest


There is a forest having a square shape with edge of 1000 meters. This forest contains 4500 oak trees having 0.5 meters in diameter. The owner of the forest wants to know if he can find a place having a rectangular place of dimensions 20 meters by 10 meters which does not intersect any of the oak trees, because he wants to build a house there. He meets a mathematician, and asks him if he can deduce the existence of such a place without going out in the field to measure things on the spot. After a few minutes and calculations, the mathematician says that he can find such a place with certainty. How did he do that?

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