What is the name of the old-time, handheld toy that consists of a plastic frame with scrambled, notched letter or number tiles, the purpose of which is to shift the tiles about within the frame until they are in sequence?

Sounds familiar - I think my bro had one back in the day. Not a clue what it was called tho.

I don't know the name, but there used to be an electronic version on Macintoshes when I was in high school. A great distraction from the lesson at hand. Any Mac users remember what it was called?

What is the name of the old-time, handheld toy that consists of a plastic frame with scrambled, notched letter or number tiles?

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".

also 'slider' puzzle or game... here's one

http://www.lilgames.com/slider_game_tiger.shtml

here's one

Heh heh.
Great fun.

I remember these from when I was a kid. There was one with a bunch of numbers in it, with the even numbers one color and the odd numbers another color. 1 through 15; the instructions said that there were certain things you could NOT do, though I cannot remember them after all these years.

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???)

Any configuration that differs from a possible configuration by one swap of tiles is impossible. Thus if

 1  2  3  4
 5  6  7  8
 9 10 11 12
13 14 15

is possible

 2  1  3  4
 5  6  7  8
 9 10 11 12
13 14 15

is not.

Welcome,Lexi - good to have you here!

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!)

In 1948-9 it enjoyed what I suspect was one of several periodic resurgences, and at that time was called the "fifteen-puzzle." I suspect it goes back to Sam Lloyd and the late nineteenth century, and maybe even before then.

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 empty

and 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.