MathDB

Each cell of the board with

2021

rows and

2022

columns contains exactly one of the three letters

T

M

, and

O

in a way that satisfies each of the following conditions:
[*] In total, each letter appears exactly

2021\times 674

of times on the board. [*] There are no two squares that share a common side and contain the same letter. [*] Any

2\times 2

square contains all three letters

T

M

, and

O

.
Prove that each letter

T

M

, and

O

appears exactly

674

times on every row.

Problem Statement