Happy Cube
Contents of this Page
 What is the Happy Cube? Notation of a Solution Figures Rectangles Some Mathematics Cube Solutions Snafooz Rubber References Happy Cube on the Internet.

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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. Small cubes 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.

 ...... 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
 ...... 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
 ...... 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.

Maxi-Cube 2x2x2
 ...... 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 cubes for all the corners, but 4 mats only have 6*4=24 corner cubes.  So it is not possible to form a maxi-cube with 4 mats.

Maxi-Cube 2x2x2
 ...... There is even a solution, which has the same colour on each side.  (Jan Verbakel, Eindhoven, 1, Seite 15)

3D Cross
 ...... 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):

Rectangles   top
Jean-Marc Dubrunfaut was looking for a rectangle formed by all 36 mats in order to use a laser cutter.
 ...... He found this 18x2  square.

There is 36= 36x1 = 18x2 = 12x3 = 9x4 =6x6 and so perhaps there are five rectangles.
 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.

 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.  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).

 ...... Benjamin Koch even found 41 solutions with six different colours instead of 21 with help of his computer.

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 side of a cube, 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

SourceForge
Happy Cube Solver

Snafooz  (The American copy of Happy Cube),  Snafooz Solutions

Thomer Gil
Happy Cube (Wirrel Warrel) Solver

Wikipedia
Happy Cube

Spanish
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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