Fill container with repeating squares - html

I love math, but I've been banging my head on this for a while.
I'm trying to fill a non square space with in HTML5 canvas with squares. I know the container width (W) and height (H). And I know the number of squares to use (n)
But the size of the square is what were trying to figure out. And how to draw it then. The squares should be just big enough to cover all the space, but it doesn't have to be sqrt(n) / sqrt(n). It should fill as much space as possible.
Any ideas on where to look to solve this?
Thanks!

A first estimate would be dividing the area W*H by the number of squares n. That will give you the area for each square, and taking the square root of that area will give you its length.
But that only works in cases where the rectangle can be exactly filled by these squares. If you might need some overlap beyond the rectangle, then you might have to adjust either the lengths or the number of squares. So suppose you want to cover your rectangle (i.e. fill a slightly larger rectangle) with no more than n squares, choosing the squares as small as possible under these circumstances. Do the above computation. Suppose that tells you that you'll need 3.75 rows and 6.23 columns of squares. Then you know that more rows or columns will require more than n squares. So you'll have to assume 3 rows and 6 columns. You can compute square lengths of H/3 and W/6 and take the larger of these.

Your scenario often is unsolvable.
For example, consider a 2 x 3 area. You can't fit either 5 or 7 squares into this area.

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http://jsfiddle.net/EwTjD/1/
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