MathDB

6

Part of 1973 IMO Longlists

Problems(1)

At least three triangles have integer areas

Source: IMO LongList 1973 - P6

6/6/2011
Let Pi(xi,yi)P_i (x_i, y_i) (with i=1,2,3,4,5i = 1, 2, 3, 4, 5) be five points with integer coordinates, no three collinear. Show that among all triangles with vertices at these points, at least three have integer areas.
geometryanalytic geometrylinear algebramatrixpigeonhole principlecombinatorics proposedcombinatorics