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Isn't it just "Sliding Tiles" or "Sliding Tile Puzzle", Lexi?
There's also a version (with which I'm more familiar, and which is more for kids, perhaps) where you end up with a simple picture. I think this is known as (fanfare) a "Sliding Picture Puzzle".
Heh heh.
Great fun.
But it was something like end up with all of the odd numbers in order above all the even numbers in order:
1 3 5 7
9 11 13 15
2 4 6 8
10 12 14 .
Anyway. You could NOT get them to move into the configuration, though you could take the puzzle apart and put them into that configuration.
But did this mean you could not get it back into the base configuration:
1 2 3 4
5 6 7 8
9 10 11 12
13 14 15 ?
In the years since then, I have read a mathematical proof as to why you could not go from one configuration to the other, but due to advancing years I cannot (what the HELL are we talking about???)
TEd
5 6 7 8
9 10 11 12
13 14 15is possible
2 1 3 4
5 6 7 8
9 10 11 12
13 14 15is not.
And in the magazine catering for the multiplicity of Amstrad PCW users, back in the old days, I picked up a similar word puzzle in Basic.
The program didn't work, any more than did most of the other puzzle programs in that magazine over the years, and debugging them to get them operational (and sometimes to improve them) was one of the ways in which I learnt how to programme in Basic - a very useful learning tool (but I never could solve the tile puzzle - even when it was working fine!)
Because of odd/even parity considerations (I really don't know the technicalities, but that's what it boils down to), half of the configurations that can be depicted cannot be achieved by sliding the tiles, so there was the "Impossible" configuration,15 14 13 12
11 10 9 8
7 6 5 4
3 2 1 emptyand many others not presented, including Faldage's above. Exchange any two adjacent tiles, though, and the polarity is reversed, and now all the "impossible" configurations are available, but the other family has become entirely impossible without another swap.
There were variations with letters and, later, pictures; the Apple puzzle came as a still-later incarnation. If there are two superficially identical tiles, then "all" arrangements can be done.
With practice and a well-lubricated puzzle, an adept eight-year-old could make any possible arrangement within a minute or less. Not unlike the Rubik's Cube manipulators of thirty years later, less an order of magnitude of difficulty, of course.
Edit: google, under "Sam Lloyd and Fifteen-Puzzle," gives a bunch of hits, including this one
http://www.maths.soton.ac.uk/~gan/MA203/puzzles.html
which I haven't had a chance to play around with yet but seems to explore the 15-Puzzle and others as illustrations of group theory, and which ought to have some more rigorous discussion of impossibility if that's what's wanted. (If not, some of the other sites brought up should.) It also has implementations of various puzzles as Java applets, if that is appealing.
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