On: AI-assisted proof of optimal packing for 11 squares

[ohyoutravel]

I am not a mathematician. Why can a square of s = N not usually fit N * N unit squares? For example S = 4, one would naively (I guess) think it could fit 16 unit squares (4 * 4), but if I’m reading the above correct the actual solution is 15 (with what looks like a unit-square-sized space left over). Same for S = 5, and S = 6, but not for S = 2, which fits the expected 4 unit squares.

[robinhouston → ohyoutravel]

They've just excluded square numbers because (as you noted) the solution is obvious. Except 4, for some reason.