17 Piece puzzle cube problem
kans...@hotmail.com
A friend of mine has a 17 piece wooden block puzzle which assembles to
a cube, fitting in a box. There are 6 2x2x3 blocks, 6 2x1x4 blocks and
5 1x1x1 blocks.
He's had the thing since Christmas 1998 and still can't get the
solution.
Has anyone seen this puzzle before? A link to a web site with details
or a solution would be hugely appreciated.
Many thanks for any help or leads.....
Kansalis.
Sent via Deja.com http://www.deja.com/
Before you buy.
Nick Wedd
>A friend of mine has a 17 piece wooden block puzzle which assembles to
>a cube, fitting in a box. There are 6 2x2x3 blocks, 6 2x1x4 blocks and
>5 1x1x1 blocks.
The 12 larger blocks all have two even dimensions. Therefore every
vertical or horizontal 5x5 "slice" of the completed cube includes an
even number of cubelets from these larger blocks, and one odd cubelet.
There are 15 such slices.
So work out first where you are going to put the odd cubelets, and then
fit the others in among them.
Nick
--
Nick Wedd ni...@maproom.co.uk
Steve Strickland
> Hi,
>
> A friend of mine has a 17 piece wooden block puzzle which assembles to
> a cube, fitting in a box. There are 6 2x2x3 blocks, 6 2x1x4 blocks and
> 5 1x1x1 blocks.
>
> He's had the thing since Christmas 1998 and still can't get the
> solution.
>
> Has anyone seen this puzzle before? A link to a web site with details
> or a solution would be hugely appreciated.
>
> Many thanks for any help or leads.....
>
> Kansalis.
>
>
> Sent via Deja.com http://www.deja.com/
> Before you buy.
Send me details of the pieces and the dimensions of the box and I'll find
the solution.
Use this format where 1's are a cubie and 0's are a blank:
0 1 0
1 1 1
0 1 0
1 1 1
1 1 1
1 1 1
0 1 0
1 1 1
0 1 0
Steve
--
Steve Strickland, Puzzlecraft
st...@puzzlecraft.com
www.puzzlecraft.com
Tim Hunt
>
> Hi,
>
> A friend of mine has a 17 piece wooden block puzzle which assembles to
> a cube, fitting in a box. There are 6 2x2x3 blocks, 6 2x1x4 blocks and
> 5 1x1x1 blocks.
>
> He's had the thing since Christmas 1998 and still can't get the
> solution.
>
> Has anyone seen this puzzle before? A link to a web site with details
> or a solution would be hugely appreciated.
>
> Many thanks for any help or leads.....
Hint:
.
.
.
.
.
.
.
.
.
You are trying to make a 5x5x5 cube. This means that you can think of
the finished cube as 5 layers of 25 cubelets.
If you take either a 2x2x3 block or a 2x1x4 block, then this must
contribute an even number of cubelets to each layer. Therefore you muct
have one of the 1x1x1 blocks in each horizontal layer.
Similarly you must have one of these small cubes in each layer parallel
to the front face, and one of these small cubes in each layer parallel
to a side face. One way to do this is to have these small cubes arranged
along a body diagonal of the 5x5x5 cube that you are trying to build.
A simpler but related puccle is to build a 3x3x3 cube out of three 1x1x1
blocks and six 2x2x1 blocks.
Tim.
--
Tim Hunt, PhD Student, Department of Applied Mathematics
and Theoretical Physics, Cambridge University, U.K.
Member of the Cambridge Go Club and 2 dan.
http://www.cam.ac.uk/CambUniv/Societies/cugos/
David Eppstein
> A friend of mine has a 17 piece wooden block puzzle which assembles to
> a cube, fitting in a box. There are 6 2x2x3 blocks, 6 2x1x4 blocks and
> 5 1x1x1 blocks.
Hint: chg gur 1k1k1'f nybat gur qvntbany orgjrra gjb bccbfvgr pbearef.
--
David Eppstein UC Irvine Dept. of Information & Computer Science
epps...@ics.uci.edu http://www.ics.uci.edu/~eppstein/
Glenn C. Rhoads
>
> A friend of mine has a 17 piece wooden block puzzle which assembles to
> a cube, fitting in a box. There are 6 2x2x3 blocks, 6 2x1x4 blocks and
> 5 1x1x1 blocks.
>
> solution.
>
> Has anyone seen this puzzle before? A link to a web site with details
> or a solution would be hugely appreciated.
>
> Many thanks for any help or leads.....
hint:
Consider any layer of the finished cube.
The layer contains 25 1x1x1 sub-cubes. No matter how you place
a 2x2x3 or a 2x1x4 block, such a block will contribute an even
number of sub-cubes to the layer. That means every layer must
contain an odd number of 1x1x1s. There are 15 layers in total
(5 parallel to the top and bottom, 5 parallel to the front and
back, and 5 parallel to the left and right sides) 5 1x1x1s,
and each 1x1x1 is in three different layers. Thus, each layer
must contain exactly 1 1x1x1 piece. Figure out how to place
the 1x1x1s so that each layer contains exactly one of them and
you are practically home free.
kans...@my-deja.com
> > a cube, fitting in a box. There are 6 2x2x3 blocks, 6 2x1x4 blocks
and
> > 5 1x1x1 blocks.
> Send me details of the pieces and the dimensions of the box and I'll
find
> the solution.
Steve,
As I said above there are 6 2x2x3, 6 2x1x4 ans 5 1x1x1 pieces. There
are no irregular-shaped pieces at all. They fit (supposedly) into a
5x5x5 cube.
Thanks for your reply.
Kansalis
Steve Strickland
I'll run it this weekend and let you know.
Glenn C. Rhoads
st...@puzzlecraft.com (Steve Strickland) wrote:
> In article <8onooc$sab$1...@nnrp1.deja.com>, kans...@my-deja.com wrote:
>
>> are no irregular-shaped pieces at all. They fit (supposedly) into a
>> 5x5x5 cube.
> I'll run it this weekend and let you know.
Oh come on. Why use a computer program on such an easy puzzle?
You can pretty much deduce the location of every piece. I wrote
down the solution in pen and I don't even have the pieces in
front of me.
Fact 1: Each of 15 layers of the cube (5 layers in each of the
three perpendicular directions) must contain exactly one 1x1x1
piece.
Reason: The simple parity argument already mentioned a few times.
The most obvious way of achieving this is to place the 1x1x1s along
a main diagonal of the cube but there are other ways.
Fact 2: Each of the 1x2x4s must be placed so that its 2x4 rectangle
is in an outer face of the cube and furthermore, each of the outer
faces must contain exactly one such 2x4 rectangle.
Reason: There must be a 1x1x1 piece in each second layer. What piece
can fill the adjacent cubicle in the outer layer? A 2x2x3 piece
can't fit and we can't use a 1x1x1 without violating fact 1. Therefore
it must be a 1x2x4 oriented so that the 2x4 rectangle is in the
outer face. This is true for each of the 6 outer faces and there
are precisely 6 1x2x4s. Fact 2 follows.
Fact 3: From the reasoning in fact 2, we see that of the 8 cubicles
in a second layer adjacent to the outer 1x2x4, 1 of these cubicles
is filled by a 1x1x1 piece. 6 of the other cubicles must be filled
by a 2x3x3 and one must be filled by part of a 1x2x4.
Reason: left as an exercise (I'm too lazy to write it out)
Fact 4: Each 1x2x4 in an outer layer fills up all of two rows/columns
except two cubicles. These cubicles must be filled with a 1x1x1 piece
and part of a 1x2x4.
Reason: left as an exercise.
Now the bottom layer must have a 1x2x4 oriented with a 2x4 rectangle
in the bottom face. There are essentially two distinct ways of
doing this. For one of the placements, its not hard to see that the
above constraints cannot be satisfied which leaves only one
possibility. This placement and the above constraints force the
locations of half the pieces. The other half is symmetric and
voila! you are done. Now go solve your puzzle.
Rizki Fadillah
www.uhamka.ac.id
<a href="https://uhamka.ac.id">rizki</a>
<a href="https://uhamka.ac.id">rizki</a>