We give an example of a set $P$ of $3n$ points in $\Bbb R 3$ such that, for any partition of $P$ into triples, there exists a line stabbing $\Omega(\sqrt n)$ of the triangles determined by the triples.
@article{118736, author = {Boris Aronov and Ji\v r\'\i\ Matou\v sek}, title = {On stabbing triangles by lines in 3-space}, journal = {Commentationes Mathematicae Universitatis Carolinae}, volume = {36}, year = {1995}, pages = {109-113}, zbl = {0831.52011}, mrnumber = {1334418}, language = {en}, url = {http://dml.mathdoc.fr/item/118736} }
Aronov, Boris; Matoušek, Jiří. On stabbing triangles by lines in 3-space. Commentationes Mathematicae Universitatis Carolinae, Tome 36 (1995) pp. 109-113. http://gdmltest.u-ga.fr/item/118736/
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