I was just thinking. has anybody ever tried to make a magic type puzzle out of triangle shaped tiles? Would it be possible to string such shaped tile together so it would work? Would ordinary Rubik's magic tiles cut diagonally work? What about other shapes?

Hmmm. Interesting idea.

Initially, I'm thinking that nothing will work other than a square, but I could well be wrong.

Magics are build in loops, as far as I can tell. Each piece has two neighbours. Each join of two pieces can take one of two shapes via the hinge transfer system Rubik ingeniously designed. A sample:



|-----|-----|
| A | B |
| | |
|-----|-----|

The above becomes one of the following, depending on the pieces you've chosen to examine:

|-----| |-----|
| A | | B |
| | | |
|-----| OR |-----|
| B | | A |
| | | |
|-----| |-----|



If the pieces were triangular, the two neighbours would share a side... which means there would have to be six fishing wires running through the grooves there, wouldn't it? That sounds to me like it would either get tangled or simply not even work.

I've got a bunch of magic tiles at home, but don't know if I'd want to start sawing them apart to try this idea. Figuring out how to string a regular magic is hard enough!

I forget the name of the guy who was creating new magic shapes a while back. He would probably have some insightful thoughts on this one.

Sandy

Let me try those diagrams again:



|-----|-----|
| A | B |
| | |
|-----|-----|

The above becomes one of the following, depending on the pieces you've chosen to examine:

|-----| |-----|
| A | | B |
| | | |
|-----| OR |-----|
| B | | A |
| | | |
|-----| |-----|



Sandy

Magic with hexagonal tiles exist.
I think, that tiles having odd number of edges, create a parity problem. It is impossible to design a stringing scheme, which works.

But I'll tell you an old story.
When I was a freshmen at Mathematics (1975), I got a sliding piece puzzle Taken (or Fifteen). Our favorite discussion topic usually was a generalisation of some idea. So I tried to do the same with the puzzle. Since raising dimension (cube, etc.) was trivial way, I proposed to change the grid from squares to triangles. But the tiles were the main obstacle on the way to mechanical puzzle. Only a few years later I've found a solution: tetrahedron shaped "tiles".