MathDB

Erick stands in the square in the 2nd row and 2nd column of a 5 by 5 chessboard. There are \

1 bills in the top left and bottom right squares, and there are \$5 bills in the top right and bottom left squares, as shown below.

\begin{tabular}{|p{1em}|p{1em}|p{1em}|p{1em}|p{1em}|} \hline \$1 & & & & \$5 \\ \hline & E & & &\\ \hline & & & &\\ \hline & & & &\\ \hline \$5 & & & & \$1 \\ \hline \end{tabular}

Every second, Erick randomly chooses a square adjacent to the one he currently stands in (that is, a square sharing an edge with the one he currently stands in) and moves to that square. When Erick reaches a square with money on it, he takes it and quits. The expected value of Erick's winnings in dollars is

m/n

, where

and

are relatively prime positive integers. Find

m+n$.

Problem Statement