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        riddles >> easy >> Assembling a Rubik's Cube 
        
(Message started by: tseuG on Jul 12^th, 2004, 1:21pm)

Title: Assembling a Rubik's Cube
Post by tseuG on Jul 12^th, 2004, 1:21pm

A 3x3x3 Rubik's cube can be made from 27 smaller cubes. Suppose we joined 2 smaller cubes to form a 2x1x1 cuboid. There would be 13 such pieces and a 1x1x1 piece would be left behind. The question is, can we assemble a Hollow Rubik's Cube using these 13 pieces so that there is a hole at the center?

Title: Re: Assembling a Rubik's Cube
Post by towr on Jul 12^th, 2004, 2:10pm

::[hide]no.
It's similar to putting dominos on a chessboard with opposite corner squares missing..
[/hide]::

Title: Re: Assembling a Rubik's Cube
Post by Grimbal on Jul 12^th, 2004, 2:21pm

I also thought it has more to do with domino and chess than about the Rubik's cube's mechanism.

Title: Re: Assembling a Rubik's Cube
Post by tseuG on Jul 12^th, 2004, 7:18pm

Right, I had that solution in mind as well but I think there is another one, may be using a different method. I used to know that sometime back. I was hoping it would turn up here.

Title: Re: Assembling a Rubik's Cube
Post by rmsgrey on Jul 13^th, 2004, 4:39am

The solution people have been hinting at is:
::[hide]
Every 2*1*1 block must either be a corner cube and an edge cube or a face cube and an edge cube - either way, every block must include an edge cube. Since there are only 12 edge cubes, you can only fill in 24 of the 26 cubes wanted.
[/hide]::

As an aside, an actual Rubik's cube is made of 21 pieces - 8 corners, 12 edges and a sort of cross shaped piece that makes up the 6 face centers and the center of the cube. Each of the 20 outer pieces has projections which together form a (rough) sphere inside the cube which is how the mechanism works. Actually trying to construct a Rubik's Cube out of cubes would make the mechanism much harder to work.

Title: Re: Assembling a Rubik's Cube
Post by tseuG on Jul 13^th, 2004, 5:33am

Thanks a lot! That's it I guess. By the way, I mentioned Rubik's cube as it was the first thing that came to my mind. This puzzle obviously doesn't have much to with it's real purpose.

Title: Re: Assembling a Rubik's Cube
Post by Icarus on Jul 21^st, 2004, 9:05pm

My first thought on reading the puzzle was "yes - I have one". The puzzle is called "the bandaged cube", and is made from an ordinary cube by gluing adjacent sub cubes together. The combinations restrict possible moves at each position to 2 or 4 or 6, which makes it very difficult to establish a standard means of solving.

But after reading towr's reply, I recalled that one of the pieces consists of an edge connected to two centers.