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Prove there exists a monochromatic triangle in space

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October 4, 2010
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Problem Statement

(SWE1)(SWE 1) Six points P1,...,P6P_1, . . . , P_6 are given in 3−3-dimensional space such that no four of them lie in the same plane. Each of the line segments PjPkP_jP_k is colored black or white. Prove that there exists one triangle PjPkPlP_jP_kP_l whose edges are of the same color.
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