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{\bf Walter Stromquist}
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{\bf Packing 10 or 11 Unit Squares in a Square}
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Let $s(n)$ be the side of the smallest square into which it is possible pack $n$ unit squares.  
We show that $s(10)=3+\sqrt{1\over 2}\approx3.707$ and that $s(11)\geq2+2\sqrt{4\over 5}\approx3.789$.
We also show that an optimal packing of $11$ unit squares
 with orientations limited to $0$ degrees  or~$45$ degrees has side 
$2+2\sqrt{8\over 9}\approx3.886$.  These results prove Martin Gardner's 
conjecture that $n=11$ is the first case in which an optimal result requires a non-$45$ degree packing.

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