MathDB

A moving particle starts at the point

\left(4,4\right)

and moves until it hits one of the coordinate axes for the first time. When the particle is at the point

\left(a,b\right)

, it moves at random to one of the points

\left(a-1,b\right)

\left(a,b-1\right)

, or

\left(a-1,b-1\right)

, each with probability

\tfrac{1}{3}

, independently of its previous moves. The probability that it will hit the coordinate axes at

\left(0,0\right)

\tfrac{m}{3^n}

, where

m

and

n

are positive integers, and

m

is not divisible by

3

. Find

m+n

Problem Statement