MathDB

In an

2023\times 2023

grid we fill in numbers

1,2,\cdots,2023^2

without duplicating. Find the largest integer

M

such that there exists a way to fill the numbers, satisfying that any two adjacent numbers has a difference at least

M

(two squares

(x_1,y_1),(x_2,y_2)

are adjacent if

x_1=x_2

and

y_1-y_2\equiv \pm1\pmod{2023}

y_1=y_2

and

x_1-x_2\equiv \pm1\pmod{2023}

).
Proposed by chengbilly.

Problem Statement