MathDB

6

Part of 1983 Austrian-Polish Competition

Problems(1)

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

Source: Austrian Polish 1983 APMC

4/30/2020
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.
3D geometrylinesperpendicularcombinatorial geometrycombinatoricsgeometry