Stochastic process problem, thank you!

1. (11 points) Go is a board game that has been invented in China more than 2,500 years ago. A standard Go board has 19x 19 grid of lines, containing 361 points. The players take turns placing the stones on the vacant intersections (points) of a board. Now suppose we play a boring game in the following way: we only keep a "corner" of the Go board i.e a board with only 4x4 grid of lines; place a stone on the top left intersection and then move the stone to any adjacent intersection along the grid of lines with uniform probability in each step. What is the expected number of steps until the stone returns to the left top inter