Abstract
Several different approaches to the multi-peg Tower of Hanoi problem are equivalent. One of them is Stewart's recursive formula ¶¶\( S (n, p) = min \{2S (n_1, p) + S (n-n_1, p-1)\mid n_1, n-n_1 \in \mathbb{Z}^+\}. \)¶¶In the present paper we significantly simplify the explicit calculation of the Frame-Stewart's numbers S(n, p) and give a short proof of the domain theorem that describes the set of all pairs (n, n1), such that the above minima are achieved at n1.
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