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 Post subject: Custom Magic???/
PostPosted: Tue Apr 09, 2002 1:37 am 
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?


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 Post subject: Re: Custom Magic???/
PostPosted: Tue Apr 09, 2002 1:40 am 
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Joined: Thu Jan 24, 2002 1:10 am
Location: Toronto, Canada
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


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 Post subject: Diagrams
PostPosted: Wed Apr 10, 2002 1:40 am 
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Joined: Thu Jan 24, 2002 1:10 am
Location: Toronto, Canada
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


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 Post subject: Odd edged tiles
PostPosted: Fri Apr 12, 2002 2:56 pm 
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Joined: Thu Dec 16, 1999 9:31 am
Location: Kaunas, Lithuania
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".


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