The problem widely known as Moser's Square Packing Problem asks for the smallest area $A$ such that for any set $S$ of squares of total area $1$, there exists a rectangle $R$ of area $A$ into which the squares in $S$ permit an internally-disjoint, axis-parallel packing. It was formulated by Moser in 1966 and remains unsolved so far. The best known lower bound of $\frac{2+\sqrt{3}}{3}\leq A$ is due to Novotn\'y and has been shown to be sufficient for up to $11$ squares by Platz, while Hougardy and Ilhan have established that $A < 1.37$. In this paper, we reduce Moser's Square Packing Problem to a problem on a finite set of squares in the following sense: We show how to compute a natural number $N$ such that it is enough to determine the value of $A$ for sets containing at most $N$ squares with total area $1$.
翻译：众所周知,Moser的“广场包装问题”要求最小的面积为1美元,因此,对于总面积为1美元的任何固定的方块,存在一个以美元为单位的矩形美元区块,其中以美元为单位的方块允许内部分离,轴面平行包装。它由Moser 于1966年提出,至今仍未解决。最著名的“Moser”的“平方块”下限值为$frac{2 ⁇ sqrt{3 ⁇ 3 ⁇ 3 ⁇ leq A$,这是Novotn/'y的产物,据显示,它足以满足Platz最多为11美元的方块,而Hougardy和Ilhan则规定,该方块值 < 1.37美元。在本文中,我们将Moser的“平方块包装问题”减少到一定的一组方块上的问题,其含义如下:我们如何计算出一个天然值为$N$,这样就可以确定在最大面积为1美元的方块上所含的方块的价值。
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