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2011 OIM Problems/Problem 6

Revision as of 15:02, 14 December 2023 by Tomasdiaz (talk | contribs) (Created page with "== Problem == Let <math>k</math> and <math>n</math> be positive integers, with <math>k \ge 2</math>. In a straight line there are <math>kn</math> stones of <math>k</math> diff...")
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Problem

Let $k$ and $n$ be positive integers, with $k \ge 2$. In a straight line there are $kn$ stones of $k$ different colors such that we have $n$ stones of each color. A "step" consists of exchanging positions of two adjacent stones. Find the smallest positive integer $m$ such that it is always possible to achieve, with at most $m$ steps, that the $n$ stones of each color remain followed if:

1. $n$ is even, 2. $n$ is odd and $k = 3$

~translated into English by Tomas Diaz. ~orders@tomasdiaz.com

Solution

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See also

OIM Problems and Solutions

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