Ready, Set, Move 1, Move 2, ...
Ever try to solve the Rubik's Cube? If few positions look familiar, it is because there are only 43,252,003,274,489,856,000 possibilities.
Question 1: Can you verify the above number of possibilities? That is, how can it be calculated?
Question 2: Suppose you could produce any position in 5 seconds....how long would it take (in years?) for you to look at every position? What if it took you one second per position?
Question 3: Read Arthur C. Clarke's The Nine Billion Names of God. What is the connection of this short story to the Rubik's Cube?