Maximum sum for column
Source: Turkey JBMO TST 2024 P2
May 13, 2024
combinatorics
Problem Statement
A real number is written on each square of a chessboard. It is given that the sum of all real numbers on the board is . Then, the board is covered by or dominos such that there isn't any square that is covered by two different dominoes. For each domino, Aslı deletes numbers covered by it and writes on one of the squares and the sum of the two numbers on the other square. Find the maximum number such that after Aslı finishes her moves, there exists a column or row where the sum of all the numbers on it is at least regardless of how dominos were replaced and the real numbers were written initially.