MathDB
1000 x 1000 chessboard

Source: Polish MO Recond Round 1987 p3

September 9, 2024
combinatoricsChessboard

Problem Statement

On a chessboard with dimensions 1000 by 1000 and squares colored in the usual way in white and black, there is a set A consisting of 1000 squares. Any two fields of set A can be connected by a sequence of fields of set A so that subsequent fields have a common side. Prove that there are at least 250 white fields in set A.