for which n can the nxn board be colored black in a finite number of steps
Source: 2009 Puerto Rico Team Selection Test p6
October 23, 2021
combinatoricsColoringboard
Problem Statement
The entries on an × board are colored black and white like it is usually done in a chessboard, and the upper left hand corner is black.We color the entries on the chess board black according to the following rule:
In each step we choose an arbitrary × or × rectangle that still contains white entries, and we color these three entries black.For which values of can the whole board be colored black in a finite number of steps