Problem

Source: 2009 Puerto Rico Team Selection Test p6

Tags: combinatorics, Coloring, board



The entries on an $ n$ × $ n$ 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 $ 2$×$ 3$ or $ 3$× $ 2$ rectangle that still contains $ 3$ white entries, and we color these three entries black. For which values of $ n$ can the whole board be colored black in a finite number of steps