10 checkers on a 8x8 board
Source: III May Olympiad (Olimpiada de Mayo) 1997 L1 P3
September 17, 2022
combinatorics
Problem Statement
On an board, checkers have been placed, each occupying a square. On each square without a token, a number between and is written, which is equal to the number of tokens placed on its neighboring squares. Neighboring cells are those that have a side or a vertex in common. Give a distribution of the tiles that makes the sum of the numbers written on the board the greatest possible.