I think there is an error with the r = 7.5 test case. By the definition of the problem, it should be 177, not 172. The working solutions use a mesh that is not on integer grid points.
I also got 177 for r=7.5 as well using (the cody unfriendly) two for loops.
@Michael_C. and @James, Thank you! I have indeed overlooked that edge case. The problem is now fixed. (The "for" loops are unnecessary).
Yaroslav, you are certainly correct that for loops are not needed. I just used them to confirm that my answer using the "no-for-loop-required algorithm" was correct before commenting on the problem. My similar problem (Cody problem 1387) only used integer radii.
Thanks for the correction!
Back to basics 26 - Keywords
Compute a dot product of two vectors x and y
Insert zeros into vector
Return area of square
Shifted Hexagonal Tiling Dots in a Circle
Volume of a Simplex
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