Spring 2020 Team Round Problem 26
Source:
August 22, 2020
Problem Statement
A magic board can toggle its cells between black and white. Define a pattern to be an assignment of black or white to each of the board's cells (so there are patterns total). Every day after Day 1, at the beginning of the day, the board gets bored with its black-white pattern and makes a new one. However, the board always wants to be unique and will die if any two of its patterns are less than cells different from each other. Furthermore, the board dies if it becomes all white. If the board begins with all cells black on Day , compute the maximum number of days it can stay alive.