How many games can be played on a 64 square board?

This is a bit of a tricky question! It depends on what kind of game you're talking about. Here's why:

* No game is defined: There's an infinite number of games you could create on a 64 square board. Think of chess, checkers, Go, or even something totally new!

* Game rules matter: The number of possible games depends entirely on the rules. For example:

* In chess, the number of possible moves grows exponentially with each turn.

* In checkers, the number of possible positions is much smaller than chess, but still massive.

* A simple game where you just move a single piece around the board has far fewer possibilities than a complex strategy game.

If you're asking about the number of possible positions:

* Assuming no rules: If we just consider the board and a single piece, the piece could be in any of the 64 squares, so there are 64 possible positions.

* With rules: If you add rules (like moving pieces in certain directions, capturing pieces, etc.), the number of possible positions would drastically change.

To get a more specific answer, you need to specify:

1. What kind of game are you thinking about?

2. What are the rules of the game?

Let me know, and I can help you figure out the number of possible games or positions!