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Prove that

Source: Kosovo TST 2015 Q4

March 30, 2015
combinatoricspigeonhole principle

Problem Statement

Let P1,P2,...,P2556P_1,P_2,...,P_{2556} be distinct points inside a regular hexagon ABCDEFABCDEF of side 11. If any three points from the set S={A,B,C,D,E,F,P1,P2...,P2556}S=\{A,B,C,D,E,F,P_1,P_2...,P_{2556}\} aren't collinear, prove that there exists a triangle with area smaller than 11700\frac{1}{1700}, with vertices from the set SS.
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