Imagine a maze created in a m by n grid Assume that there is

Imagine a maze created in a m by n grid. Assume that there is a unique path from any cell to any other cell. What is the total length of the walls in the maze as a function of m and n? For example, below is a 2 by 2 grid with the required path property and the total length of walls is 9. Explain your answer.

Solution

Grid of 2 x 2 has total lenght of walls is 9.

Total length of walls of m x n grid :

length of side walls = mxn

length of wall in middle = n/2

Total length of walls = mxn +n/2