Chikkee, you're correct. I missed the 9 in size #3. But I also see that there are two borders around the big size, making 41, as sewandsew says.
Thanks tiredeyes, Chikkee, hooknstitch, mpilnadyful, stevem and sewandsew!! If you see some we have missed, let us know!

There are five different sizes of squares: 8x8, 6x6, 4x4, 2x2, and 1x1.
Square size ..... Count
8x8 ..... 1 (or 2 if you count the thin border on the outside)
6x6 ..... 4
4x4 ..... 9
2x2 ..... 18
1x1 ..... 8

answer from my son the math genius, unless someone else know exactly. That's our final answer! LOL

Pretty certain the answer is 35 - certainly, it's got to be an odd number, because all the smaller squares are in fours, with two twos - then there's the overall square (4 units by 4), so odd.

I see 40, in 5 different sizes. 1 in size #1 (big), 4 in size #2 (taking up 9 of the smaller squares), 9 in size #3 (taking up 4 of the smaller squares), 18 in size #4 (each small square), and 8 of size #5 (tiny squares).

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