Consider the problem of solving the 8-puzzles.

a. Give a complete problem formulation in the style of Chapter 3.

b. How large is the reachable state space? Give an exact numerical expression.

c. Implement a solution to the problem according to your formulation using: h1 = 0, h2 = misplaced tiles, h3

= Manhattan distance, h4 = h3 + 40, h5 = h3 + 1000, and h6 = h3 + Rand(40,1000).

d. Consider the final state shown in Figure 3.28. Form a set of 4 instances of the problem by randomly

crafting 4 initial states. Add the initial state shown in Figure 3.28 to the set, resulting in total of 5

instances. Run your program against each instance using the three different h’s to reach the final state.

e. Report the following for each instance:

1. The initial state

2. The optimal number of steps to solve the problem, and the corresponding solution sequence.

3. The number of nodes expanded using each h.

4. The number of steps to solve the problem, and the corresponding solution sequence using each h.

f. Repeat (e) again 4 times with different order of actions tired.

g. Comment on your observations.

Note that, Find the attached reference