Eternity II

You may remember a few months ago I wrote a blog post about Competitions and their Prizes in which I addressed the issue of scepticism surrounding competitions and give-aways.  It was mostly centred around the idea that the majority - if not all - of the entrants generally don't hear who won [except the winner of course], and in the case of dodgy or potentially fraudulent competitions if no-one actually won it would be quite hard to prove that.

Enter Christopher Monckton and TOMY who created a board game, or rather more accurately described as a jigsaw, or to be completely pedantic, a tessellation puzzle.  The board consisted of 256 empty squares, each square could have one of 256 tiles placed on it.  Each tile had 4 possible orientations and no two tiles are identical.  In raw terms this provides 4^256 [4 to the power of 256] possible permutations, needless to say to try them all by hand would be insane.  The entire board though can be seen as a 512 bit encryption key.  In theory all of this should be possible, and the challenge in solving the board would be quite hard.

Now the problem comes when you want to prove it can be done, as that proof in itself was the point of the game, much to the same end that a bedlam cube is a toy you can't put back in its box without playing with it because putting it in the box is the game.  I digress.  I am talking here about proof by demonstration, not a mathematical proof - as in the case of the latter this puzzle is by all means possible.  The point of this post is to highlight something about this particular Game, and the competition that was associated with it.  The Game maker offered £1 million or $2 million at the time Eternity II was launched on the 28th of July 2007 to whomever completed the puzzle.  Several "scrutiny dates" were arranged where entrants could submit solutions, the closest winning a cash prize and the first complete solution winning the jackpot.  Almost 4 years passed by and the final scrutiny date came and passed on the 31st of December 2010 and the makers announced that no-one had managed to complete the puzzle and the prize went unclaimed.  Any individual attempting to make a submission from then on would be ignored.  Effectively the competition ended without a winner.  So even if you managed to complete it now, there would be no prize for doing so, you might not even get a reply from the manufacturer if you tried to get it verified.

It is now 2012 and over a year has passed since the final scrutiny date and the makers of the puzzle have not published the correct solution.  Now as far as I am concerned, until they do, this entire competition was a scam.  I will happily admit it was not, when I see the solution.  However as the contest has ended and they have not published a solution it is not unreasonable to suggest that no solution exists.  For those of you reading now and dreaming of ways to solve the problem, it is a lot more complex than I have made out in this post.  The very nature of this game is incredibly deceptive, it seems incredibly simple at first but the more you look into it and the more you think about trying to solve it and the more you realize it has been designed to be incredibly hard to complete.  Therein lies the problem, as it is evident that every measure was taken to make the puzzle as hard as possible to solve the question of whether it can actually be solved becomes more prevalent.  It is not like a jigsaw where you could place 255 pieces down be left with one that doesn't fit and call shenanigans, the pieces can move around freely on the board, completing 255 pieces and having 1 remaining that didn't fit would only imply the other 255 are not in the correct pattern.

I am a programmer and I would consider myself to be a bit of a geek.  I had a go at the puzzle but after a few minutes playing it and studying the pieces with my flatmates we had a short discussion that more or less amounted to "we're not meant to do this by hand" - in other words, we're expected to try and create some form of solution, either from a mathematical approach or by creating a program that can solve the puzzle.  The latter I can vouch is not as simple as you would think and even if you could manage to create a program the amount of data it has to process is immense and would take several lifetimes - even for some of the world's most expensive supercomputers.  Truly if you solve this puzzle in Professor McGonagall's words it would be "sheer dumb luck"