[Stubbs]

Oh for a world where that'd be a compliment...

Definitely meant as a compliment!

[Drew]

I don't think there is a solution to the maze problem. This is my proof. Feel free to rip it to shreds:

Take two mazes. Maze A, and Maze B.

Suppose Maze A is a relatively simple maze from Left (East) to Right (West), the simple solution is W-N-W-S-W

i.e. it looks like this

########
#               #
     ####
########




Now suppose Maze B is infinitely long, but it solved purely by holding it in the West position i.e.

#########

#########




If one was to solve Maze B, it would be simple, but would require each position to be held for an infinite amount of time, which means you can only hold one position. This will only solve Maze B. Therefore it is impossible. I think.

[Stubbs]

An infinite maze would be unsolvable because it was, well infinite.

[Drew]

So it's ok to use an infinitely repeating sequence, but we can't have an infinite maze?

[Stubbs]

Correct

[tomtom]

The ball in the maze doesn't move just one square, it moves in the specified direction until it cannot go further... S your top sequence would work fine.. And it would work in an infinitely long maze if you were happy to wait for an infinite time

I think there may be a way, but it needs a nifty analytical solution rather than the blunt modelling tool we used...

[Jerry Morefat]

An infinite maze would be unsolvable because it was, well infinite.

Of cause it would be solvable. You'd need to use an infinite sequence.

Back to the main problem, I may be being a bit slow but in order to solve every maze, surely the only sequence which would work would be NESW NESW.....NESW and so on, and so on repeating blocks of 'NESW'.

[Stubbs]

Of cause it would be solvable. You'd need to use an infinite sequence.

As TT pointed out in the post just above yours it would take an infinite amount of time, and as such I don't think you could consider it to be 'solved'.

Back to the main problem, I may be being a bit slow but in order to solve every maze, surely the only sequence which would work would be NESW NESW.....NESW and so on, and so on repeating blocks of 'NESW'.

If you have a think about it its quite easy to come up with several mazes for which this wouldn't work.

[Jerry Morefat]

Of cause it would be solvable. You'd need to use an infinite sequence.

As TT pointed out in the post just above yours it would take an infinite amount of time, and as such I don't think you could consider it to be 'solved'.

Why not? Firstly there isn't a time component to the problem, so bringing time in seems a bit spurious. Secondly. there are countless examples of proofs which rely on infinite sequences of some sorts. One example being a Taylor series (http://en.wikipedia.org/wiki/Taylor_series)

Back to the main problem, I may be being a bit slow but in order to solve every maze, surely the only sequence which would work would be NESW NESW.....NESW and so on, and so on repeating blocks of 'NESW'.

If you have a think about it its quite easy to come up with several mazes for which this wouldn't work.

Which ones? I think I must have misinterpreted the problem if this is the case?

[Stubbs]

Hmmm how about a maze with a clockwise spiral leading to a chamber? I've not drawn it but I don't think NESW would get you out of it.

[Jerry Morefat]

Hmmm how about a maze with a clockwise spiral leading to a chamber? I've not drawn it but I don't think NESW would get you out of it.

Ah, so I was being a bit slow. Sorry, I saw some of those funky diagrams people were drawing and assumed there was one and only one possible path  and the ball couldn't go back the way it came. Ho hum.