MathDB

We consider a square board of

1000\times 1000

with

1000000

squares

1\times 1

. A piece placed on a square threatens all squares on the board that are inside a

19\times 19

square. with a center in the square where the piece is placed, and with sides parallel to those of the board, except for the squares in the same row and those in the same column. Determine the maximum number of pieces that can be placed on the board so that no two pieces threaten each other.

Problem Statement