MathDB
41 letters on a circle, each letter is A or B

Source: Tournament of Towns, Senior Ο-Level Paper, Spring 2020 , p3

June 4, 2020
combinatorics

Problem Statement

There are 4141 letters on a circle, each letter is AA or BB. It is allowed to replace ABAABA by BB and conversely, as well as to replace BABBAB by AA and conversely. Is it necessarily true that it is possible to obtain a circle containing a single letter repeating these operations?
Maxim Didin