MathDB

In the Game of Life, each square in an infinite grid of squares is either shaded or blank. Every day, if a square shares an edge with exactly zero or four shaded squares, it becomes blank the next day. If a square shares an edge with exactly two or three shaded squares, it becomes shaded the next day. Otherwise, it does not change. On day

1

, each square is randomly shaded or blank with equal probability. If the probability that a given square is shaded on day 2 is

\tfrac{a}{b},

where

a

and

b

are relatively prime positive integers, find

a + b.

Problem Statement