3n x 3n table with interesting coloring
Source: Azerbaijan 2022 JBMO TST C4
July 5, 2022
combinatoricsAzerbaijanJuniorJBMOJBMO TSTJunior Balkantable
Problem Statement
is a natural number. Given table, the unit cells are colored white and black such that starting from the left up corner diagonals are colored in pure white or black in ratio of 2:1 respectively. ( See the picture below). In one step any chosen square's white cells are colored orange, orange are colored black and black are colored white. Find all such that with finite steps, all the white cells in the table turns to black, and all black cells in the table turns to white. ( From starting point)