A city where the names of people are either A or B and 10 letters long
Source: BdMO 2022 Secondary P7
April 12, 2022
combinatorics
Problem Statement
Sabbir noticed one day that everyone in the city of BdMO has a distinct word of length , where each letter is either or . Sabbir saw that two citizens are friends if one of their words can be altered a few times using a special rule and transformed into the other ones word. The rule is, if somewhere in the word is located consecutively, then these letters can be changed to or if is located somewhere in the word consecutively, then these letters can be changed to (if wanted, the word can be kept as it is, without making this change.) For example can be transformed into (the opposite is also possible.) Now Sabbir made a team of citizens where no one is friends with anyone. What is the highest value of