MathDB

C5

Part of 2023-IMOC

Problems(1)

"I can solve this without seeing it"

Source: 2023 IMOC C5

9/9/2023
In an 2023×20232023\times 2023 grid we fill in numbers 1,2,⋯ ,202321,2,\cdots,2023^2 without duplicating. Find the largest integer MM such that there exists a way to fill the numbers, satisfying that any two adjacent numbers has a difference at least MM (two squares (x1,y1),(x2,y2)(x_1,y_1),(x_2,y_2) are adjacent if x1=x2x_1=x_2 and y1−y2≡±1(mod2023)y_1-y_2\equiv \pm1\pmod{2023} or y1=y2y_1=y_2 and x1−x2≡±1(mod2023)x_1-x_2\equiv \pm1\pmod{2023}).
Proposed by chengbilly.
combinatorics