Nerd Alert - Eternity II - (almost) impossible

This post will reveal the depths of my nerd-dom, in case any one still hasn't figured that out.

This day I purchased myself a new way to waste time - the Eternity II puzzle. The deal with this is that it is one of these math things - it has a solution, but there are so many billion-gazillion-pentillion-willion NON-solutions, that there is really almost no chance of finding a good solution. Go ahead, use computers, that is allowed. The maker of the game even offers up a two million dollar prize to the first person to correctly solve it and follow some simple instructions on mailing the solution in. The only catch, is you have to solve it before 2010 ends. It is that hard, even using banks of super fast computers, the game maker figures his odds of paying out the prize money aren't all bad.

Anything THAT crazy is of course going to appeal to my nerd side.

The puzzle is only 256 pieces, an exact square made of littler squares in a 16 by 16 grid. Each piece has a design and color on each edge that must be lined up with a matching piece on all sides, and there is a gray border that must be built around the outside edge. One piece in the middle is given to you, and you have to use that piece in that spot (which actually makes the puzzle harder).

Let's see, the middle of the puzzle is 14 pieces by 14 pieces, with one piece given. That leaves 195 pieces to place in the middle, or 195! (195 factorial) ways to place them. But of course, each piece can also be turned four different ways, so the total number of ways to build just the middle, is really (195!)*(4 to the power of 195), which is a very big number. And then the 60 pieces that make up the edge can also be placed a bunch of possible ways, so I better get working on it. I will come back to this topic again, as my efforts hopefully show some results...