Consider the problem of solving two 8-puzzles: there are two 8-puzzle boards, you can make a move on either one, and the goal is to solve both. 

a. Give a complete problem formulation. 

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

c. Suppose we make the problem adversarial as follows: two players take turns moving; a coin is flipped to determine the puzzle on which to make a move in that turn: heads puzzle one; tails puzzle two. The winner is the first to solve either puzzle. Which algorithm can be used to choose a move in this setting? 

d. In the adversarial problem, will one player eventually win if both play perfectly?