IMO Shortlist 1969 problem 58
Dodao/la:
arhiva2. travnja 2012. ![(SWE 1)](/media/m/2/7/7/2771a92393060a53a039590be1fcc4c9.png)
Six points
![P_1, . . . , P_6](/media/m/6/b/5/6b5ebb88ebca87259efc6cb08e592596.png)
are given in
![3-](/media/m/3/5/7/357a30a60199d5080f3d5073d436ba31.png)
dimensional space such that no four of them lie in the same plane. Each of the line segments
![P_jP_k](/media/m/8/b/a/8ba41658ffd68b3272cede32e2cef712.png)
is colored black or white. Prove that there exists one triangle
![P_jP_kP_l](/media/m/5/3/1/531106ecbaccc2a2a8b248996e30a070.png)
whose edges are of the same color.
%V0
$(SWE 1)$ 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.
Izvor: Međunarodna matematička olimpijada, shortlist 1969