@johncarlosbaez@mathstodon.xyz
Post #3913862
2026-07-18 15:21 UTC
Wow! If the side length of this "Sierpiński triangle" is 1, the average distance between its points is 466/885.
Double wow! The average number of moves in a shortest path between two random states in the n-disc Tower of Hanoi puzzle is asymptotically (466/885)·2ⁿ as n → ∞.
(1/n)
Replies (1)
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@johncarlosbaez@mathstodon.xyz 2026-07-18 15:22
But be careful: By "distance", I mean the length of the shortest path moving inside the Sierpiński triangle, not the usual distance between points in the plane. Also: we compute the "average" distance using the natural measure on the Sierpiński triangle, not Lebesgue measure. (2/n) https://arxiv.org/abs/math/0310109