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I really wish there were visualizations for this.

“Choose a region, where two squares don’t fit, -> 16(??)”

I consider myself literate (maybe not adept) with advanced maths, but this confuses me and requires a lot of assumptions on my end.

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A simpler way to see this is to first focus on the central region of the big square that's 0.5 units away from the edge. All squares centers must lie in this region. Break this region into a grid of 25 equally sized square tiles. Each tile is now small enough that the center of two squares can't lie within the same tile. This gives 25 choose 11 possibilities. The article instead broke this region into hexagons that were still small enough that the centers of two squares can't lie in the same hexagon. This let them use only 16 tiles, which vastly reduced the space of possibilities.

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