MathDB

A token starts at the point

(0,0)

of an

xy

-coordinate grid and them makes a sequence of six moves. Each move is

1

unit in a direction parallel to one of the coordinate axes. Each move is selected randomly from the four possible directions and independently of the other moves. The probability the token ends at a point on the graph of

|y|=|x|

\tfrac{m}{n}

, where

m

and

n

are relatively prime positive integers. Find

m+n

Problem Statement