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Given an arrangement of 
points, a Line containing just two of them is called an ordinary line.
Moser (1958) proved that at least 
lines must be ordinary (Guy 1989, p. 903).
See also General Position, Near-Pencil, Ordinary Point, Special Point, Sylvester Graph
References
Guy, R. K. ``Unsolved Problems Come of Age.'' Amer. Math. Monthly 96, 903-909, 1989.