It takes less time for you to try to read about the question than to type this comment. I know the link doesn't contain visualization, but... come on.
replyThe whole point is that you can fit more than by naively stacking them...
replyparent is changing the problem by suggesting to "pack in the 3rd dimension": lay all the squares on the same square footprint, resulting in always needing only a square with side length 1 on which all the needed "packed" unit squares are laid.
replyLook at some of the other links people have posted for optimal packings. The optimal 11 square packing looks nothing like what you're describing ("just stack the cubes next to each other").
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