The person who downvoted you must not have thought it through.
For comparison to that 10^120^ possible game states, the number of atoms in the universe is only 10^82^ and the amount of time until the "Dark Era" of the universe (after all the stars have died and even all the black holes have decayed via Hawking radiation) is only 10^114^ to 10^117^ seconds. In other words, it really is literally impossible either to build a computer big enough to store all the board states or to write them all down even if you did.