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Q lies inside the triangle P_iP_jP_k

Source: 1983 Hungary - Kürschák Competition p3

October 10, 2022
geometrycombinatoricscombinatorial geometry

Problem Statement

Given are n+1n + 1 points P1,P2,...,PnP_1, P_2,..., P_n and QQ in the plane, no three collinear. For any two different points PiP_i and PjP_j , there is a point PkP_k such that the point QQ lies inside the triangle PiPjPkP_iP_jP_k. Prove that nn is an odd number.
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