Checkered plane divided into dominoes
Source: Russian TST 2016, Day 11 P1 (Group B)
April 19, 2023
combinatoricsdominoes
Problem Statement
The infinite checkered plane is divided into dominoes. If we move any horizontal domino of the partition by 49 cells to the right or left, we will also get a domino of the partition. If we move any vertical domino of the partition up or down by 49 cells, we will also get a domino of the partition. Can this happen?