Dividing a square into equal-area rectangles

geometry combinatorics recreational-mathematics tiling discrete-geometry

Solution 1:

Sorry to poke a dead post but it was near the top of the "unanswered questions" queue for me and it's a decent problem.

Working locally should provide a good avenue of attack on this problem.

For instance, a relatively straightforward analysis (which I'll post if there is interest) yields:

$$ C(p^2) = 2\left(\sum_{k=0}^{p} {p^2-k(p-1) \choose k}\right)-1 $$

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