Unit squares intersecting all secants of a square

Abstract

Let S be a square of side length s>0. We construct, for any sufficiently large s, a set of less than 1.994 s closed unit squares whose sides are parallel to those of S such that any straight line intersecting S intersects at least one square of S. It disproves L. Fejes Tóth's conjecture that, for integral s, there is no such configuration of less than 2 s-1 unit squares. © 1994 Springer-Verlag New York Inc.