My girlfriend doesn’t like any computer games. Any computer games? Well, there’s one she does like and in fact went to the trouble of installing herself: the 11th Hour. Yes it’s old^H^H^Ha classic. But playing it together - which I have to admit is an altogether different experience on a widescreen TV with a decent stereo and a fast computer - we ran into something I missed on the first time through.

I would warn you about a spoiler, but first off the game is so old that if you haven’t played it by now, you probable never will. And besides that, what I’m about to tell you concerns an unsolvable puzzle in the game and I think you won’t mind getting the spoiler if it helps you avoid that agony. Somewhere on disc 1 (out of 4) you’ll get to a room that has a mirror in it. Looking at the mirror starts a puzzle which seems simple enough. It’s one of those typical sliding tiles puzzles, where the mirror gets divided up into 10 pieces and you have to slide them back in place using the grime on the glass as a reference.

The thing is, with any sliding piece puzzle, not any random configuration is solvable. The puzzle in the 11th Hour is a 2×5 puzzle and therefore a 10-puzzle (or 9-puzzle). You can read an article on n-puzzle solvability on Wikipedia, but what it comes down to for this puzzle can be more easily illustrated.

The 2×5 (2 rows, 5 columns) puzzle can be seen as a circle of tiles, which can be moved around clockwise and counter-clockwise. Moving a piece sideways along the top or bottom, or moving a piece vertically along either side doesn’t change the order of the pieces in the circle. When the gap is at either side, that type of move is the only possible move, so the order of tiles in the circle can’t change. For example, if the gap is in the upper left corner, you can only slide the piece to the right of in along the top, or the piece below it along the left side.

So, the only moves that actually change the order of the pieces, occur when the gap is in one of the other six positions. You can then slide a piece vertically, changing it’s relative position in the circle. Looking at it that way, you’ll notice that doing so effectively makes the piece skip 2, 4 or 6 other tiles in the circle. It can never skip an odd number of tiles. Even combining as many such moves as you like, you can never exchange two neighbouring tile without exchanging two other tiles in the same way.

The 11th Hour game mixes the parts at random however, so in about half of the cases, there will be an odd number of flipped pairs, making the puzzle impossible to solve. It took us quite a bit of sliding and hard thought to figure out that the puzzle we were looking at was actually unsolvable. After that, we simply restarted the puzzle until it gave us one which had an even number of exchanged pairs and after that actually solving it was a piece of cake.

Of course, it would never have taken so long if I’d only known about the Wikipedia article, but then again: the whole point of solving puzzles is figuring stuff like this out, I suppose. If you’re ever playing the 11th Hour though, I hope I justed saved you some frustration which I think wasn’t intended by the designer of the puzzle who may simply have been unaware of the problem.

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