Problem of the Week 1112

Counting Collinear

Given 48 points in the plane which are positioned so that 1113, but no more, distinct lines can be drawn through pairs of points, prove that at least four of the points are collinear.

Source: This week's problem is only slightly modified from The Wohascum County Problem Book by Gilbert, Krusemeyer and Larson, MAA, 1993.

© Copyright 2009 David Ehren. Reproduced with permission.