MathDB

A real number is written on each square of a

2024 \times 2024

chessboard. It is given that the sum of all real numbers on the board is

2024

. Then, the board is covered by

1 \times 2

2\times 1

dominos such that there isn't any square that is covered by two different dominoes. For each domino, Aslı deletes

2

numbers covered by it and writes

0

on one of the squares and the sum of the two numbers on the other square. Find the maximum number

k

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

k

regardless of how dominos were replaced and the real numbers were written initially.

2