MathDB
Coloring a square grid

Source:

December 28, 2006
probabilitygeometryrectanglenumber theoryrelatively prime

Problem Statement

Each unit square of a 3-by-3 unit-square grid is to be colored either blue or red. For each square, either color is equally likely to be used. The probability of obtaining a grid that does not have a 2-by-2 red square is mn\frac{m}{n}, where mm and nn are relatively prime positive integers. Find m+nm+n.