8-puzzle

In the 8-puzzle, the goal state can look as follows

  1 2
3 4 5
6 7 8

Lets say the initial state is

6 1 4
2 3 5
8 7

The problem is solved by determining the path (i.e. set of directions) the blank is moved, in the case if I move it up I have to displace at least the 5, but its also possible to displace 5 and 4 depending on how you define what happens to UP (there are multiple displacements possible - I have listed 4)

6 1 4     6 4 5     6 1 4     1 4 5 
2 5       2 1       3 5       6 3
8 3 7     8 3 7     2 8 7     2 8 7

So my question then: For this type of problem, how is the effect of UP defined? as there can be multple definitions, if you stick to 1 then you can have unsolvable puzzles...

turns out up is just up and in the example given, is the 1st transition,

the others are - (left, up, up, right, down), (left, left, up, right, right), get the idea... its about a single state change...

anyway, started revision