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l_1, l_2, l_3$ are pairwise perpendicular, and so are l_4, l_5, l_6

Source: Austrian Polish 1983 APMC

April 30, 2020
3D geometrylinesperpendicularcombinatorial geometrycombinatoricsgeometry

Problem Statement

Six straight lines are given in space. Among any three of them, two are perpendicular. Show that the given lines can be labeled ℓ1,...,ℓ6\ell_1,...,\ell_6 in such a way that ℓ1,ℓ2,ℓ3\ell_1, \ell_2, \ell_3 are pairwise perpendicular, and so are ℓ4,ℓ5,ℓ6\ell_4, \ell_5, \ell_6.
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