MathDB

In each cell of a

2019\times 2019

board is written the number

1

or the number

-1

. Prove that for some positive integer

k

it is possible to select

k

rows and

k

columns so that the absolute value of the sum of the

k^2

numbers in the cells at the intersection of the selected rows and columns is more than

1000

.
Folklore

M2555