Brute force sudoku cracker

[Gregory Bond]

My current solver does 1 level of backtracking (i.e. constant space, and 
bounded time) only, and it has been able to solve every puzzle I've 
thrown at it.  It's based on the usual logic and book-keeping for the 
most part.  (It also explains how it comes up with each answer step as 
it goes, which is handy...)

Once it gets to the stage where it needs to guess, it arranges all the 
unknowns then tries them in some arbitary order.  It saves the state, 
applies the guess (square x,y is N) and then re-applies all the logic 
rules.  There are 3 possible outcomes from here:

  - We've solved it, which is good (this happens surprisingly often....)

  - We can't solve it using this guess (so ignore this possibility, 
restore the state & try the next guess)

  - The Resulting puzzle is badly formed / inconsistant (represented by 
a python exception, naturally!) In this case, we know the guessed 
square/number is not valid, so we backtrack (restore the state before we 
made this guess), remove that possibility (x,y is N) and then apply all 
the logic rules again.  Often times, this is enough to solve, but it 
usually progreses things a little even if it doesn't solve it.

I've not yet found a (9x9) puzzle that this cannot solve.  The downside 
is that it cannot detect cases where there are multiple solutions.