Problem

Source: (2021-) 2022 XV 15th Dürer Math Competition Finals Day 2 E13

Tags: combinatorics



Write some positive integers in the following table such that $\cdot$ there is at most one number in each field $\cdot$ each number is equal to how many numbers there are in edge-adjacent fields, $\cdot$ edge-adjacent fields cannot have equal numbers. What is the sum of numbers in the resulting table?