Question 2: 118 marks] a) [4 marks] Assume we create a heuristic function h3 such that it averages the values of the misplaced tile heuristic (hl) and the Manhattan distance heuristic (h2): h3(n) 1/2 [h1(n) + h2(n)] Is it admissible heuristic? Justify your answer. b) [6 marks] Draw the state space for the tower of Hanoi where there are three disks of different sizes D1 (small), D2 (medium) and D3 (large) and three towers A, B, and C (from the left to the right in the figure). The goal is to move the disks, one at a time, so that in the final state all disks are at tower C. The constraint is that no smaller disk can be put below a larger one. The middle tower, B, can be used temporary.