True or False:

For every set S of five or more points in the plane, if every subset of five points can be covered by two lines, then S can be covered by two lines.

Extra credit: T or F: For every set S of six or more points in the plane, if every subset of six points can be covered by at most two lines, then S can be covered by at most two lines.

Source: Iranian Olympiad, 2002, Oct *Crux. Mathematicorum*, p. 347

© Copyright 2007 Stan Wagon. Reproduced with permission.