Problem

Source: KJMO 2023 P5

Tags: combinatorics



For a positive integer n(5), there are n white stones and n black stones (total 2n stones) lined up in a row. The first n stones from the left are white, and the next n stones are black. \Circle\Circle\Circlen\CIRCLE\CIRCLE\CIRCLEnYou can swap the stones by repeating the following operation. (Operation) Choose a positive integer k(2n5), and swap k-th stone and (k+5)-th stone from the left. Find all positive integers n such that we can make first n stones to be black and the next n stones to be white in finite number of operations.