In each square of a 100×100 board there is written an integer. The allowed operation is to choose four squares that form the figure or any of its reflections or rotations, and add 1 to each of the four numbers. The aim is, through operations allowed, achieving a board with the smallest possible number of different residues modulo 33. What is the minimum number that can be achieved with certainty?
number theoryboardcombinatorics