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infinite queens on an infinite chessboard (I Soros Olympiad 1994-95 R1 11.4)

Source:

August 1, 2021
combinatoricsChessboard

Problem Statement

Given a chessboard that is infinite in all directions. Is it possible to place an infinite number of queens on it so that on each horizontally, on each vertical and on each diagonal of both directions (i.e. on a set of cells located at an angle of 45o45^o or 135o135^o to the horizontal) was exactly one queen?