A few weeks ago I posted an interesting mathematical puzzle involving a randomly generated maze. The short explanation of it was, "What is the probability that a randomly generated maze will be solvable?"

After many responses and stimulating discussion, it has become clear that no one has been able to solve it. And so I took some time this weekend to work out a brute force solution. And while it is not the simple solution that I was hoping for (and am still hoping someone will discover), it is still a solution.

Unfortunately it is too complicated and contains too many formulae to include in this blog. For that reason, I have written it into a PDF file, and posted it here.

But the question remains, for a seemingly simple puzzle is there a simpler solution?

UPDATE: Shortly after posting the PDF file I discovered a possible problem with the solution, in that one of the more complicated theorems from mathematical physics which I was relying on is usually stated for systems with slightly different boundary conditions. I feel that it should work for this puzzle as well, but the proofs that I can find do not make this clear. As such, I am retracting my claim of a solution, and encourage readers to attack this problem once more.