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CIIM 2009 Problem 3

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June 9, 2016
CIIM 2009CIIMundergraduate

Problem Statement

Let r>nr > n be positive integers. A "good word" is an nn-tuple ⟨a1,…,an⟩\langle a_1,\dots, a_n \rangle of distinct positive integers between 1 and rr. A "play" consist of changing a integer aia_i of a good word, in such a way that the resulting word is still a good word. The distance between two good words A=⟨a1,…,an⟩A= \langle a_1,\dots, a_n \rangle and B=⟨b1,…,bn⟩B = \langle b_1,\dots, b_n \rangle is the minimun number of plays needed to obtain B from A. Find the maximun posible distance between two good words.
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