Question 36
An integer is written in each square of a $100\times100$ checkerboard. An allowed operation chooses four squares in one of the following layouts:
or any rotation of them, and adds $1$ to the number in each chosen square. The goal is to obtain, by allowed operations, a board with as few different remainders modulo $33$ as possible. What is the smallest number that can always be guaranteed?
or any rotation of them, and adds $1$ to the number in each chosen square. The goal is to obtain, by allowed operations, a board with as few different remainders modulo $33$ as possible. What is the smallest number that can always be guaranteed?