I think that with this kind of problem, you can process in two steps.
A first easy problem with small N (to test perms for example). And a harder problem with big N, which
oblige to find another algorithm.
Roll the Dice!
Size of this cup?
Dots in a Sphere
Number of digits in an integer
Calculate the Number of Sign Changes in a Row Vector (No Element Is Zero)
Make one vector from two others
Matrix of Multiplication Facts
Decimation - Optimized for speed
The Hills Are Alive...
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