Unit Squares Intersecting all Secants of a Square

Pavel Valtr Department of Applied Mathematics Charles University Czech Republic email: valtr@CSPGUK11.bitnet Report B 92-11 May 92

Get the report here or by anonymous ftp: 
Server: fubinf.inf.fu-berlin.de
File:   pub/reports/tr-b-92-11.ps.gz
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 T\'oth's conjecture that, for integral $s,$ there is no such configuration of less than $2s-1$ unit squares.