Chess rooks
Source: St Petersburg Olympiad 2009, Grade 9, P6
August 30, 2017
combinatorics
Problem Statement
Call a set of some cells in infinite chess field as board. Set of rooks on the board call as awesome if no one rook can beat another, but every empty cell is under rook attack. There are awesome set with rooks and with rooks. Prove, that there are awesome set with rooks.