Tiling with dominoes
Source: Tournament of Towns, 2016 Fall Tour, A Senior, Problem #2
April 22, 2017
combinatorics
Problem Statement
A natural number is written in each cell of an board. It turned out that for any tiling of the board with dominoes, the sum of numbers in the cells of each domino is different. Can it happen that the largest number on the board is no greater than ?(N. Chernyatyev)(Translated from [url=http://sasja.shap.homedns.org/Turniry/TG/index.html]here.)