### Number of possible mazes

Posted:

**Mon Apr 16, 2007 5:08 pm**Problem:

How many different combinations of mazes exits with x width and y height?

Conditions:

- Each maze must have one solution only

- Player starts at top left position

- Exit is at bottom right position

- No loops

- No isolations

Examples:

x=2 and y=2 equals 2 combinations:

(The style with a wall in the center is just to visualize the mazes better, so they don't count as real "spots". Therefore, x=2 and y=2 in the below maze)

Or

x=3 and y=2 equals 8 (or have I missed some?) combinations:

Or

Or

Or

Or

Or

Or

Or

So, how many maze combinations can be made with x width and y height?

How many different combinations of mazes exits with x width and y height?

Conditions:

- Each maze must have one solution only

- Player starts at top left position

- Exit is at bottom right position

- No loops

- No isolations

Examples:

x=2 and y=2 equals 2 combinations:

(The style with a wall in the center is just to visualize the mazes better, so they don't count as real "spots". Therefore, x=2 and y=2 in the below maze)

Or

x=3 and y=2 equals 8 (or have I missed some?) combinations:

Or

Or

Or

Or

Or

Or

Or

So, how many maze combinations can be made with x width and y height?