Can the $2000\times2000$ be colored with certain rules
Source: St. Petersburg MO 2000, 10th grade, P5
April 22, 2023
combinatoricsgridsColoringtableInvariantsgeometryrectangle
Problem Statement
Cells of a board are colored according to the following rules:1)At any moment a cell can be colored, if none of its neighbors are colored2)At any moment a rectangle can be colored, if exactly two of its neighbors are colored. 3)At any moment a squared can be colored, if 8 of its neighbors are colored(Two cells are considered to be neighboring, if they share a common side). Can the entire board be colored?[I]Proposed by K. Kohas