[ Chessboards and chess pieces $]$ [ Examples and counterexamples. Constructions ] [ Evenness and oddness

Authors: Pechkovsky A.N., Itenberg I.

Given an infinite grid paper with a cell side equal to one. The distance between two cells is defined as the length of the shortest path of a rook from one cell to another (the path of the center of the rook is considered). What is the minimum number of colors needed to color the board (each cell is colored with one color) so that two cells, located at a distance of 6, are always colored differently?

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