Unit Squares Intersecting all Secants of a Square
Department of Applied Mathematics
Report B 92-11
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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.