MathDB

26

Part of 2020 LMT Spring

Problems(1)

Spring 2020 Team Round Problem 26

Source:

8/22/2020
A magic 3×53 \times 5 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 1515 cells (so there are 2152^{15} 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 33 cells different from each other. Furthermore, the board dies if it becomes all white. If the board begins with all cells black on Day 11, compute the maximum number of days it can stay alive.