Six points
are given in
dimensional space such that no four of them lie in the same plane. Each of the line segments
is colored black or white. Prove that there exists one triangle
whose edges are of the same color.
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$(SWE 1)$ Six points $P_1, . . . , P_6$ are given in $3-$dimensional space such that no four of them lie in the same plane. Each of the line segments $P_jP_k$ is colored black or white. Prove that there exists one triangle $P_jP_kP_l$ whose edges are of the same color.
Školjka