Problem

Source: Mathcenter Contest / Oly - Thai Forum 2012 sl-10 https://artofproblemsolving.com/community/c3196914_mathcenter_contest

Tags: number theory, prime numbers, combinatorics



The table size $8 \times 8$ contains the numbers $1,2,...,8$ in each amount as much as you want provided that two numbers that are adjacent vertically, horizontally, diagonally are relative primes. Prove that some number appears in the table at least $12$ times. (PP-nine)