Consider the 3-square random process we discussed in class. We found the state transition diagram and the transition probability matrix, they are in the notes.

(a) Modify the diagram and matrix so that when the puzzle is solved, it no longer leaves the solved state. It just stays there.

(b) Use MATLAB to answer the following question for the modified process: At time k=0 the puzzle is in state 7. We repeatedly flip a coin to decide whether to move horizontally or vertically (p = q = 0.5). After N moves, the probability to be in the solved state is 50%. Find N.