>
> To eliminate the idea of rotation, we could just say this:  given  
> the neighborhood:
>
> +--+
> |12|
> |43|
> +--+
>
> Change to:
>
> +--+
> |23|
> |14|
> +--+
>
> or:
>
> +--+
> |41|
> |32|
> +--+
>
> There's a 50% chance to go either way.
>
> James Edward Gray II
>
these examples are rotation. Anything else would be permutations.  
Could be done numerous ways. Array sorts, Rot13 (with only 4 digits.)  
etc..