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).
Pi Estimate 1
How many rectangles in a grid ?
Placing Beads Neatly in a Box
NCHOOSEK - Time Optimization
Hexagonal numbers on a spiral matrix
Which permutation is it?
expand intervals vol.3
Optimum Egyptian Fractions
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