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Problem 6 of Third round

Source: XI International Festival of Young Mathematicians Sozopol 2022, Theme for 11-12 grade

September 9, 2022
combinatorics

Problem Statement

A mixing of the sequence a1,a2,…,a3na_1,a_2,\dots ,a_{3n} is called the following sequence: a3,a6,…,a3n,a2,a5,…,a3n−1,a1,a4,…,a3n−2a_3,a_6,\dots ,a_{3n},a_2,a_5,\dots ,a_{3n-1},a_1,a_4,\dots ,a_{3n-2}. Is it possible after finite amount of mixings to reach the sequence 192,191,…,1192,191,\dots ,1 from 1,2,…,1921,2,\dots ,192?
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