onic (consistent) heuristics for varying problems. a) An example of an 8-puzzle is given in the figure below. The goal is to move the tiles one at a time until the goal is reached, in which the tiles are ordered. Given a state n, prove that the following heuristic for the 8-puzzle is admissible: h(n)=i=18Manh(Ti,n,Ti,g) where Ti,n is position of tile i in state n,Ti,g is the position of tile i in the goal state, and Manh(Ti,n,Ti,g) is the Manhattan Distance between tiles Ti,n and Ti,g