What is the Happy Cube?
... ...
|
The puzzle Happy Cube consists of 6 mats
of foam coloured blue, green, yellow, orange, red, and violet. Here
you can see the blue mat.
Each mat has six 5x5 pieces surrounded by a frame. Little cubelets are
cut irregularly along the edges. It is possible to put the six 5x5 pieces
together to a 5x5x5 cube, if you find special positions. |
If you look at the scan of the mat, you see that many hands have touched
the pieces ;-). The frame is still clean.
... ... |
For each colour there are various levels of difficulty of solving.
The blue mat is easy to solve, the purple one is the most difficult.
The Happy Cube was designed by Dirk Laureyssens in 1986. It received
several names such as the I.Q.ube, de Wirrel Warrel Kubus, CocoCrash
and Cube-it.
Dirk Laureyssens' variants are:
The Little Genius, the Profi Cube, the Marble Cube (work together
with Happy Cube)
Further there are the Planet Cube, Snafu, Snuzzle, and Crico. |
Notation of a Solution top
...
4'/5'16/2/3
|
You can number the six pieces from 1 to 6 on the front side. You can
recognize the front side by a little circle in one corner on the left (blue:
left up). You name the rear side of 1 1', corresponding 2' to 6'.
If you find a solution, you form a base of the cube, which is a cross.
Make sure that 1 is upright in the middle. Then the description is definite.
You also number the other mats for the solutions. Notice the little
circle on the left showing the front side. |
Figures (Simple Cubes below) top
Box 1x1x2
... ...
|
You can put together a figure of two cubes with the help of the blue
and green mats.
You take 10 pieces of 12.
2 pieces are left. |
Box 1x1x3 top
... ...
|
You can put together a figure of three cubes with the help of the blue,
green and yellow mats.
You take 14 pieces of 18.
4 pieces are left. |
Box 2x1x2 top
... ...
|
You can put together a figure of four cubes with the help of the blue,
green and yellow mats.
You take 16 pieces of 18.
2 pieces are left. |
Maxui-Cube 2x2x2 top
... ...
|
You can put together a figure of 2x2x2-cube with the help of all the
6 mats. You take 24 pieces of 36. 12 pieces are left.
Theoretically you can build it with 5 mats.
If you use 4 mats, you get 24 pieces. That is sufficient. But you can
show, that you need 26 cubelets for all the corners, but 4 mats only have
6*4=24 corner cubelets.
So it is not possible to form a maxi-cube with 4 mats.
|
Maxi-Cube 2x2x2top
... ...
|
There is even a solution, which has the same colour on each side.
(Jan Verbakel, Eindhoven, 1, Seite 15) |
3D Cross top
... ... |
If you want to build the figure on the left, first you have to put
five pieces together to form four open cubes. The middle piece is at the
bottom. (You have to keep the orientation in the space.) Then you form
a ring of the four open cubes.
At last you form two open cubes by the pieces on the very right and
put them at the bottom and at the top of the ring. |
on the left
|
at the back
in front
|
on the right
|
at the top
at the bottom
|
You take 30 pieces of 36. Six pieces are left.
1x2x3-box with a collar
It is nice to include the frame. Here is a solution by Jan Verbakel
(1, page 21):
Some Mathematics top
Every piece has 4 edges. If you turn a piece, you have 4 more edges.
You write down a pattern of an edge with a sequence of 0 and 1. This
is a number with 5 digits in the binary system. If there is no little square,
you write 0. If there is a little square, write 1. This method will be
shown by piece number 4. In the drawing the number is related to the edge
near to the number.
|
In this way you can fix the number of the 6x6x4x2 = 288 patterns of the
edges for all the mats in a chart.
top
decimal
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
number of the patterns: |
binary
00000
00001
00010
00011
00100
00101
00110
00111
01000
01001
01010
01011
01100
01101
01110
01111
10000
10001
10010
10011
10100
10101
10110
10111
11000
11001
11010
11011
11100
11101
11110
11111
. |
blue
-
-
-
-
16
2
-
-
-
-
10
4
-
-
-
-
-
-
-
-
2
4
-
-
-
-
4
6
-
-
-
-
8 |
green
-
-
-
-
14
4
-
-
-
-
10
4
-
-
-
-
-
-
-
-
4
2
-
-
-
-
4
6
-
-
-
-
8 |
yellow
-
-
-
1
8
6
-
1
-
-
12
4
-
-
-
-
-
-
-
-
6
2
-
-
1
-
4
2
1
-
-
-
12 |
orange
-
-
1
1
10
1
3
-
1
1
6
5
3
-
-
-
-
-
1
-
1
6
-
-
1
-
5
2
-
-
-
-
16 |
red
-
-
1
1
10
3
2
-
1
-
8
3
2
1
-
-
-
-
-
1
3
2
1
-
1
1
3
4
-
-
-
-
18 |
purple
-
-
2
3
6
4
1
3
2
-
6
3
1
1
-
-
-
-
-
-
4
-
1
-
3
-
3
2
3
-
-
-
17 |
sum
-
-
4
6
64
20
6
4
4
1
52
23
6
2
-
-
-
-
1
1
20
16
2
-
6
1
23
22
4
-
-
-
. |
You can see:
> Only 22 of 32 possibilities are used to form an edge (black letters).
> All the pieces with x000x or x111x are avoided (red letters).
> The four pairs (00100,11011), (00101,11010), (01010,10101)
and (01011,10100) going together appear frequently (240 of 288). They occur
at every colour with one exception. They are used exclusively at
blue and green (bold letters)
> Patterns like x11xx, xx11x, x00xx or xx00x do not occur at blue and
green.
> Two pairs are the same, red4/blue3 und orange4/violett4.
Symmetries top
You find a cube easier, if there is symmetry.
.
Symmetric edges:
Symmetric pieces with two axes
Symmetric pieces with one axis |
blue
36
2
1 |
green
32
1
2 |
yellow
24
0
0 |
orange
24
0
2 |
red
24
0
1 |
violet
14
0
0 |
Cube Solutions top
The main problem is making a cube with one colour. Students found all
solutions by trying. I give only one drawing for one colour. Symmetric
solutions are counted once.
One of three solutions
4'/5'16/2/3
|
One of five solutions
4'/516/2/3'
|
One of five solutions
4'/3'15'/2'/6
|
The only solution [orange ;-)]
5/4'12/6'/3
|
.The only solution
5/6'12/4/3'
|
.The only solution
3/412/6'/5'
|
The blue and the green cube can be easily done. The blue cube is more difficult,
because the pieces 1, 2 and 3 must follow in the same sequence for every
solution.
I would give the yellow cube the lowest degree of difficulty. The edges
00011 (piece 2) and 11100 (piece 3) fit together, piece 1' complete them
to a half cube. Then it is not far away to the whole cube.
It is very difficult to solve the purple cube, because you are often
on the wrong track.
All solutions:
blue, 3 solutions: 4'/5'16/2/3, 2/4'15/6'/3',
4'/612/5'/3
green, 5 solutions:
4'/516/2/3', 6/213/4/5, 2/6'13/4/5, 3/415/6'/2, 3'/514'/2/6'
yellow, 4 (5) solutions:
4'/3'15'/2'/6,
6/3'15/2'/4', (6/3'15'/2'/4',) 6/4'12'/5'/3', 4'/612'/5/3'
orange, 1 solution:
5/4'12/6'/3
red, 1 solution: 5/6'12/4/3'
violet, 1 solution: 3/412/6'/5'
... ... |
You can also form a mini cube of six pieces with different colours
(on the left).
There are computer results about forming a mini cube with different
colours in article 1 (11pp):
19 mini cubes with the distribution 3+3 (2 colours), 88 with
2+2+2 (3 colours), 21 with 1+1+1+1+1+1 (6 colours). |
Snafooz top
Snafooz is an American copy with six models. It goes into competition
with the Happy Cube family.
... ...
|
Snafooz is common in the USA.
There are also six mats. A 6x6-square forms the basis of a piece, not
a 5x5-squares like at Happy Cube.
(Drawing by Xandur, USA)
|
Rubber top
... ... |
There is a puzzle from Japan, which uses a 4x4-square
as a basis. The six pieces, which form a cube, show animals because of
shape and decoration. The material is known from the rubber. That is what
the pieces should be.
My puzzle has only Japanese letters.
In the article (1) you find, that you can read
SEED, PLASTIC ERASER, MADE IN JAPAN on the plastic box:. |
References top
(1) Jan de Geus, Joop van der Vaart: Happy Cubes (Wirrel Warrel), Cubism
For Fun (CFF), published by the Nederlandske Kubus Club (NKS), Part 50/4,
(1999)
Happy Cube on the Internet
top
German
Reich der Spiele
Happy
Cube
Wikipedia
Happy
Cube
English
Dirk Laureyssens
The homepage of
the inventor of Happy Cube
Happy Cube
SourceForge
Happy Cube Solver
Snafooz (The American copy
of Happy Cube), Snafooz
Solutions
Thomer Gil
Happy Cube (Wirrel Warrel)
Solver
Toine de Greef
Several solutions
of the 2x2x2 cube with 5 mats only
Wikipedia
Happy
Cube
Spanish
NN
Evalandia.Soluciones Cococrash
Feedback: Email address on my main page
This
page is also available in German.
URL of
my Homepage:
http://www.mathematische-basteleien.de/
©
1999 Jürgen Köller
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