Perhaps I am misinterpreting, but it seems to me that some of your testsuite solutions are incorrect. For example, for N=5 I seem to be getting 19 instead of 27 cubes entirely within the sphere. I double-check using this code: x=rand(1e6,3); r=sum((x-.5).^2,2)
You are totally right. I've generated answers using my solution, which was wrong. My fault is I haven't examined it any other way. Considering N=5, there could fit inside the sphere only a 3x3x3 cube, but its space diagonal is 3*sqrt(3) which is bigger than 5, the diameter of sphere. So, there cannot be more than 27-8=19 cubes inside. Thanks, for pointing that out, Alfonso!
Fixed & rescored now. It leads now to smaller-size answers. Consider the fact that for some N (for example 6) there are some quasi-cubes containing a very small amount of peel from those ultra-thin-peel-sweet-juicy-ideal-oranges ;-)
DNA N-Gram Distribution
Angle between Two Vectors
Calculate the height of an object dropped from the sky
Who has power to do everything in this world?
Another colon problem
Optimum Egyptian Fractions
How many solutions has this problem?
Don't Try, give up and return NaN.
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