Betting money on sum of areas
Source: Sharygin geometry olympiad 2016, grade 10, Final Round, Problem 4.
August 5, 2016
combinatoricsgeometryareagamegame strategy
Problem Statement
The Devil and the Man play a game. Initially, the Man pays some cash to the Devil. Then he lists some triples consisting of positive integers not exceeding . After that, the Devil draws some convex polygon with area and pays to the Man, the sum of areas of all triangles . Determine the maximal value of which guarantees that the Man receives at least as much cash as he paid.Proposed by Nikolai Beluhov, Bulgaria