In a $5$ by $5$ grid, the outer perimeter of the grid, which leaves a $3$ by $3$ grid in the middle, is designated as out. Pepe the frog starts at the middle space and randomly moves up, left, down, or right one space at a time. What is the average number of moves taken by Pepe until he goes out?
Recursive Grid Movement
Ananyabrata Barua Asked question