Consider the problem of solving two 8-puzzles.

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: the two players take turns moving; a coin is flipped to determine the puzzle on which to make a move in that turn; and the winner is the first to solve one puzzle. Which algorithm can be used to choose a move in this setting?

d. Give an informal proof that someone will eventually win if both play perfectly.

Write a program that prints the day number of the year, given the date in the form month-day-year. for example, if the input is 1-1-2006, the day number is 1; if the input is 12-25-2006, the day number is 359. the program should check for a leap year. a year is a leap year if it is divisible by 4, but not divisible by 100. for example, 1992 and 2008 are divisible by 4, but not by 100. a year that is divisible by 100 is a leap year if it is also divisible by 400. for example, 1600 and 2000 are divisible by 400. however, 1800 is not a leap year because 1800 is not divisible by 400.