Given an arrangement of points, a line containing just two of them is called an ordinary line. Dirac (1951) conjectured that every sufficiently
set of 
noncollinear points contains at least 
ordinary lines (Borwein and Bailey 2003, p. 18).
Csima and Sawyer (1993) proved that for an 
arrangement of points, at least 
lines must be ordinary. Only two exceptions are known
for Dirac's conjecture: the Kelly-Moser configuration (7 points, 3 ordinary lines;
cf. Fano plane) and McKee's configuration (13 points,
6 ordinary lines).
Silva and Fukuda conjectured that for any noncollinear, equally distributed, line-separable arrangement of points of two colors, there is at least one bichromatic ordinary line. Finschi and Fukuda found a unique nine-point counterexample in a study of 15296266 distinct configurations (Malkevitch).
Ordinary Points." Disc. Comput. Geom. 9,
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Problem." Hederl. Adad. Wetenach. 51, 1277-1279, 1948.Dirac,
G. A. "Collinearity Properties of Sets of Points." Quart. J. Math. 2,
221-227, 1951.Erdős, P. "Problem 4065." Amer. Math.
Monthly 51, 169, 1944.Felsner, S. 
Points." Canad. J. Math. 1,
210-219, 1958.Lang, D. W. "The Dual of a Well-Known Theorem."
Math. Gaz. 39, 314, 1955.Malkevitch, J. "A Discrete
Geometrical Gem."