Comments by "" (@zachrodan7543) on "A Lifelong Mathematical Obsession" video.

  1. Another way to justify nC0=1 is that nCk could be interpreted as Given a set with n elements, how many subsets are there with k elements. Every set has the empty set as a subset, and since a set is only defined by its elements, there is exactly one empty subset.
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  2. Like you, i first concieved of this problem as a child, and also in terms of n=5... although in my formulation it was always just about ways of arranging the numbers while separating consecutive numbets. I then spent all of last summer quarter working out the answers for up to n=8... by creating an adjacency graph, counting the allowable hamiltonian paths and circuits on those graphs, and then using some symmetry to get the final counts (there are as many ways to start at 1 and end at 2 as there are ways to start at n and end at n-1; you can go either direction on a path, and you can start at any point on a path that is a closed loop) Probably doesn't help my attempts that i apparently undercounted, at least in the case od n=6, where I only found 76 ways to do it... [Insert mathematically flavored profanity here]
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