Problem

Source: Mexico National Olympiad Mock Exam 2021 P5

Tags: combinatorics



Consider a chessboard that is infinite in all directions. Alex the T-rex wishes to place a positive integer in each square in such a way that: No two numbers are equal. If a number m is placed on square C, then at least k of the squares orthogonally adjacent to C have a multiple of m written on them. What is the greatest value of k for which this is possible?