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?