we are suppose to choose a method of solving this thing - not just start at a state and then try and figure out all possible states to follow that selection.

Hence, we choose to solve either LINE by LINE or ROW by ROW - also we are NOT to show any state that resolves to ILLEGAL. hence if you are to insert a 3 somewhere (and that 3 is going to cause it to be ILLEGAL), just skip everything down that path.

basically we are limiting our solution states - eg. by choosing row by row solution - you will have only two states in the first row that are legal. There after, the forst row is considered COMPLETE, then you start with row2.

My mistake was to fill in one value in ROW1, and then try and make up all possible choices in all other rows and columns thereafter. I ended up with 70 states (halfway through the combinations from the 2nd state) and then finally decided that I needed some advice :-)]]>

imagine the following

2 1 a b

4 c d e

f g h 4

i j 1 k

this is the initial state,

a possible next state would be

2 1 4 b

4 c d e

f g h 4

i j 1 k

where a = 4

OR even with a = 3 (nothing prohibits this, if this is your first choice - even though you might find it wrong later).

but seeing as though a=3 is NOT the correct state, a=4 is the only option (hence we should only show this state - this is what we are asked to do - to show only legal states)

if so, we could start at any of the possible 11 blank blocks, Enter the correct value, and then follow any of the remaining 10 blocks - entering the value. Then any of the remaining 9 blocks entering the correct value.

eg. two possible initial states

2 1 4 b

4 c d e

f g h 4

i j 1 k

2 1 a 3

4 c d e

f g h 4

i j 1 k

then a possible 2nd state

2 1 4 3

4 c d e

f g h 4

i j 1 k

which would overlap coming from one of the previous two.

Is this what we are aiming at? or am I mad?]]>

thx again for participating :-) :-)

see the thing is, they ask ONLY LEGAL moves to be shown in the state space.

thus

As soon as you reach a fail move you stop that branch

in based on that, we can never fail... hence we will never stop in a branch because of an illegal move. We will simply be entering all the legal moves in different combinations.. which to me sounds kind of silly.]]>

Anybody else? Come on!!!!! Some of you must be working on this by now and have some thoughts to share, right or wrong.]]>

they ask for the full state diagram, showing only legal states...

if I take the initial state as the 2x2 diagram they provide, and then try to draw out each possible legal state (one move at a time), im going to end up with the combination of the first 11 moves, each followed by a combination of the next 10 moves, 9, 8, 7. Hence a tree structure that has the same number of nodes in each branch... each of which will eventually get to the goal state...

Am I correct? or am i missing something here...

help would be appreciated, finding this kind of difficult.]]>