### 23rd Putnam 1962

**Problem A1**

5 points lie in a plane, no 3 collinear. Show that 4 of the points form a convex quadrilateral.

**Solution**

If the convex hull has 4 or 5 vertices, then we are done. If not, then two of the points, say D and E, must lie inside the triangle ABC formed by the other three. DE must intersect just two of AB, BC and CA. Suppose that it does not intersect AB. Then the four points A, B, D, E form a convex quadrilateral.

23rd Putnam 1962

© John Scholes

jscholes@kalva.demon.co.uk

5 Feb 2002