I've talked with people about the amount of chess moves and all combinations and it is an extremely large number. You could calculate it by hand, but then you run into the issue like how people were trying to calculate more and more digets of pi. It could take decades. This is why computers are so extremely useful. The combinations of chess moves was actually an unsolved equation, among others like number of soduku game combinations and so on.

This was an interesting example to use since you could say any beach in the world and it would have an unfathomable number of particles of sand. This number even overshadows the known number of stars, planets, asteroids, etc in space. Really shows how little the scope of numbers we deal with. Computers deal with someone comparable numbers, with 2^64 very common today and even 2^128 as well.