Talk:Nine dots puzzle
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Higher dimensions
[edit]Added a brief introduction to the extension of the classic planar version of the puzzle to higher dimensions. I avoided citing some references, but I can provide many of them by request (please, let me know).
About the stated solution for the (n=2) k-dimensional case, you can find the proof here Solution for the n=2 case (k=2,3,4,...).
Generally speaking, is it trivial to show that (n^k-1)/(n-1) is a lower bound for any pair of positive integers (n, k) (e.g., if n=4 and k=3, no solution with less than (4^3-1)/(4-1)=21 can exists for the given problem).