>Danny:  I do not understand your algorithm - could you shed some more
(high-level) light on what it is doing?

Sure. The idea is that the optimal size will always be an exact fraction of
either the width or the height. So what we do is drop down by multiples of
these until we get to the first size that will contain N or more squares. At
any particular width, we keep track of the two 'next-smallest' widths and
drop down to the largest of these. Run through the algorithm with a few
sample numbers and it should make sense.

It may be that there's a more algebraic approach. The problem is, though,
that there is no simple relationship between floor(x), floor(y) and
floor(xy), which would be needed to come up with any truly useful solution.
In the end, it turns into quite a complex optimisation problem, and given
that the brute force algorithm is actually pretty fast, it hardly seems
worth the effort :)

Danny

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