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Unit Squares Intersecting all Secants of a Square

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

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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.