posted
I like to play with a wooden puzzle I have. It consists of the 12 pieces you can make when you'd glue 5 small squares together in every possible way. So you would have a piece like this:
xxxxx
and this:
xxxx x
and this
xxx xx
and so on.
Anyway, it is not very hard to put the pieces together in the box again. But you can also make all sorts of three dimensional figures out of it. I used to have a booklet with examples, but I lost it. Now I am trying to make this figure:
bottom: 6 x 6 first floor: 4x4 in the middle of the 6x6 second and third floor: 2x2 in the middle of the 4x4
Well, now the question: I don't succeed, how could you prove mathematically whether it is possible or not to make this figure?
Posts: 1247 | Registered: Apr 2000
| IP: Logged |
posted
It's 12 pieces of 5 blocks each, Ic, for a total of 60 blocks.
Base has 36 blocks, first floor has 16 blocks, and the next two floors have 4 blocks each - for a total of 60 blocks.
Each piece has a different configuration of 5 blocks, sort of like Tetris (only with 5 squares instead of 4... Pentris, perhaps?).
He's trying to make a certain configuration of three dimensional pieces (made up of 5 blocks per pice) into a three dimensional tower shape, I think.
If there's a mathematical way to prove it can or can't be done, I don't know what it is. Without the exact configuration of each of the 12 pieces, I don't know if that's even possible.
Posts: 3960 | Registered: Jul 2001
| IP: Logged |
quote:Originally posted by Icarus: And there's no (significant) third dimension?
As I understand it Icarus, Each of the blocks is a cube.
I think to get the 12 permutations you have to add a third dimension
X(2X)X __X
XX(2X) X
XX(2X) ___X
where the 2X means that there is a two blocks stacked in the third dimension. But now I'm getting more than 12 permutations.
Posts: 12591 | Registered: Jan 2000
| IP: Logged |
posted
Yeah!!! Thank you so much for the links aspectre! I tried to find them myself ofcourse, but I couldn't find anything, that's why I posted my question here.
Posts: 1247 | Registered: Apr 2000
| IP: Logged |
posted
If only I'd have known those things are called Pentominos! Here is another link Pentomino's They even have a computer program for solving pentomino problems. Hmm.
Posts: 1247 | Registered: Apr 2000
| IP: Logged |
posted
(The following is my understanding of a field I don't work in; may contain inaccuracies.) The little blocks are called pentominoes, and are a fairly popular field for amateur mathematicians; however, it is my understanding that it is quite difficult to prove any general results with them, because the tools don't really exist to do so. (And probably won't until someone with some good formal maths training gets annoyed and really takes a full-on swing at it.) All you can do is play around with visualising it, which is fine for constructive solutions but doesn't do so well at proving there are none.
Posts: 10645 | Registered: Jul 2004
| IP: Logged |
Printer-friendly view of this topic
![[Confused]](confused.gif)
![[Smile]](smile.gif)
![[Big Grin]](biggrin.gif)
