May be I am wrong. But, are test 7 and 8 correct?
Looks like 7 and 8 should use fit(x), not fit(x,y).
Sorry for that. Fixed now.
Every test is correct. The problem with the circle packing algorithm is precision. Set the precision wrongly and we will miss a lot of circles (It was fun to revisit this kind of problem). And btw, the upper bound for circle packing in the plane is pi/sqrt(12) of the total area. Ignore the spheres in the question, it's a circle packing problem ("easy" version, since we already have the radii).
Most nonzero elements in row
Count from 0 to N^M in base N.
Sum all integers from 1 to 2^n
Create a dictionary
Calculate the area of a triangle between three points
Open coded lock.
Pernicious Anniversary Problem
How many solutions has this problem?
Polite numbers. N-th polite number.
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