Last year I became fascinated by squared squares and its history and theory – e.g. see this page on the algebraic and network methods of constructing them. I wrote a program to find if there were packings for squares of side . Packings? I don’t know what to call them – unlike the business of squaring squares and rectangles, I’m not concerned about the shape of the boundary. The program found packings for 9, 25 and 49 squares, and there’s a simple regular pattern that can be extended to work with any odd .
Here’s the 7×7 = 49 square version
The 9×9 = 81 square version.
The 11×11 = 121 square version.