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Problem 85


Problem 85


Counting rectangles

By counting carefully it can be seen that a rectangular grid measuring 3 by 2 contains eighteen rectangles:

Although there exists no rectangular grid that contains exactly two million rectangles, find the area of the grid with the nearest solution.


数长方形

如果数得足够仔细,能看出在一个3乘2的长方形网格中包含有18个不同大小的长方形,如下图所示:

尽管没有一个长方形网格中包含有恰好两百万个长方形,但有许多长方形网格中包含的长方形数目接近两百万,求其中最接近这一数目的长方形网格的面积。