The Puzzling Story of SOMA A printable page to introduce SOMA. 14 Nov 2018

Problems worthy of attack, Prove their worth by hitting back. (Piet Hein)
From time to time, man have tried to construct a threedimensional puzzle.
In no circumstances has it, succeeded so well as with the SOMA cube, invented by the Danish Author Piet Hein.

The Danish Author Piet Hein conceived the idea of the SOMA cube in 1936, during a lecture of Quantum physics by Werner Heisenberg (Father of the un-certain principle). When the lecture entered the subject: A room divided by cubes. Piet Heins easily movable imagination grasped, in a lightening flash this unusual geometric theory.

• If you take all irregular shapes that can be formed by combining no more than four cubes, all the same size and joined at their faces. - These shapes can be combined to form a larger cube.

These are all the possible combinations of 1, 2, 3 and 4 cubes.

• You can visualize what is meant by "irregular" by noting that in such a figure, you can join two points on the figure with a line which lies outside the figure (except for the endpoints.) Thus, a figure formed by three cubes joined in a line is not irregular. .

As the lecture continued, Piet Hein convinced himself quickly, using some hasty sketches on a piece of paper, that seven shapes, which in total contained 27 cubes, would let itself be combined to a larger cube of the dimensions 3 x 3 x 3.
When the lecture was over, he glued 27 dices together to form the 7 shapes, and was quick to get the idea tested in practice.

It is important to note that Mr. Hein did NOT begin with a cube, and cut it up to form the puzzle. He visualized the pieces first, then considered whether they would form a cube.

Piet Hein called his set of figures SOMA.

He eventually arrived at the seven pieces making up the Soma Cube. It all went from there as he began working with the various shapes managing to create very impressive structures. It was soon thereafter noticed by Piet and his fellow Soma experimenters that the act of arranging the pieces into shapes became very fun, however, very addicting.

After having worked with the figures for some days, many find that the shapes have been them so wellknown, that they can solve SOMA-problems in their head.
All, who have participated in these tests, have insisted in continuing to play with the cubes, after finishing the tests.

The Soma cube consist of seven different polycubes, the threedimensional analogues of polyominoes. The polycubes can be fitted together to form the Soma cube in 240 ways.
As well as a large number of Soma shapes: the pyramid, the bathtub, the dog and so on.

One obvious activity is to try to find several possible solutions. It soon becomes clear that a method of recording solutions must be found. One method is to look at the completed figure from the top down, and record the number of the piece each component belongs to, using the piece numbers. Once you have discovered a figure of your own, record it using the method.

SO to do the NOTATION, the SOMA pieces are named 1,2,3,4,5,6,7 or V,L,T,Z,A,B,P
I know it is confusing to have both a number AND a letter for a piece, but it DO help when writing down figures, and if you are using just a single SOMA set (As most people do) then you can chose to use numbers or letters.
Now to solve a SOMA puzzle, you must read the solution code for the puzzle. Let's examine the figure number 007 "THE BED"

The written solution looks like this:
```      /SOMA007                     /SOMA007 using letters
/7.....6/7733366             /P.....B/PPTTTBB
/5.....1/7443261             /A.....V/PZZTLBV
/5.....1/5544222             /A.....V/AAZZLLL```
The first line is simply the identification /SOMA007
The '/' is a separation character used by SOMA Solver software.
The next lines show the figure starting from the top, as slices of cubes. The top slice is at the left..
You may inserte spaces in front of the '/' if you find that to be easier to read. But Solver software do not allow spaces.

If you look at the bottom layer (at the right), look at the first line, you see the number '3', this is the 'T' shaped piece laying flat.
To the left of this you see the number '7', which is the 'P' Pyramid shaped piece, and if you look at the left side table, you see that this piece extend one of its cubes into the top layer.

SOMA: (Sanskrit) Is an Euforic plant extraction, used in ancient India as a narcotic - SOMA narcotics forgot time and place.

Martin Gardner says:
The number of beautiful figures, that may be built using the 7 SOMA shapes seem to be unlimited, when I wrote my article in the magazine 'Scientific American', I only figured that a few readers would take the trouble of making their own set of SOMA shapes. But I was wrong. Thousands of readers mailed me drawings of new SOMA models, and many claimed that they no longer had any spare time, after they were caught by the SOMA.

Scientific American brought columns on SOMA in Sep 1958, July 1969, sep 1972.
In August 1998 they presented the figures Dog, Pyramid, Stairs, Chair, Steamer, Castle, Skyscraper(Impossible), Bathtub, Tunnel, Sofa, Well and the Wall.

Teachers produced SOMA-sets for their classes. Psycologists started using SOMA at their tests. SOMA enthusiasts made SOMA sets to friends in hospitals, and for christmas gifts. The charme of SOMA is, for a large part, I would think, that one only uses 7 shapes. One is not overwhelmed by a complicated material.

Piet hein says:
It is a beautiful humour of the nature, that the 7 simplest irregular combinations of cubes, can be recombined to the cube again. The multitudes of unity is again producing the unity. This is the worlds smallest philosophic system, and that surely must be an advantage.

 The LEGO SOMA. A simple way to make your own SOMA Cube is by using Legos.

The SOMA puzzle is covered extensively on the internet.
Both as search for the words "SOMA puzzle". and on "Youtube"

Should you find interest in knowing more about SOMA, then try visiting "Thorleif's SOMA pages"
at: https://www.fam-bundgaard.dk/SOMA/SOMA.HTM

This SOMA puzzle site has 360 MegaByte, over 15000 figures, over 142 Newsletters,
original Danish and Parker Bros. booklets, history, Scans of original newsletters, theories, proofs,
An advanced SOMA puzzle solving program, ... and a lot more!

SOMA figures This initial group of figures was presented in the original SOMA manual.
 A001 THE CUBE N001 Step2 P001 Cube parts P002 Double 1
 P003 2*1/2CUBE A002 aeroplane A003 dog A004 robot
 A005 crystal A006 castle 1 A007 bed A008 tower
 A009 chair A010 bathtub A011 castle 2 A012 snake
 A013 tunnel A014 gallow A015 cornerstone A016 sofa
 A017 steamer A018 well A019 monument A020 tomb

The SOMA Solutions in this list show the figures as each level is sliced, from the top and down.
Try to build the figures above, but look below if you get stuck. A001 The final cube.
 ```4 5 2 7 5 5 7 7 6 4 1 2 4 6 5 7 6 6 One Solution, of 240 1 1 2 4 3 2 3 3 3 ```
N001
Even if you use only 2 blocks, difficult shapes are possible.
 ```2 2 2 . 6 . 6 6 2 . 6 . ```
P001 (Soma pairs 1)
If you start with N001, it will be particularly difficult to build the cube.
 ```. . 2 2 | 3 . . 3 1 1 3 4 1 6 6 2 6 | 5 . . 3 . . 4 4 7 . . 2 6 | 5 . . 5 5 7 4 7 7 ```
P002 Double size (Soma pairs 2)
Remove the smallest piece, and build a double size version.
 ```1 1 7 2 6 6 7 7 4 6 1 3 2 2 2 7 4 4 6 3 3 5 4 3 5 5 5 ```
P003 The cube in halves (Soma pairs 3) by Piet
This is a special way of building the cube, First build two shapes, then combine then to the cube.
 ```2 2 . 4 2 5 4 2 5 4 . . 4 . . 7 5 5 . . . 7 . . 7 7 . 2 2 3 4 2 5 4 2 5 + = 4 6 3 4 6 3 7 5 5 1 . . 1 3 . 3 3 3 6 6 3 7 1 1 7 7 1 . . . 1 6 . 6 6 . . . . . . . 6 . . ```
A002 The Aeroplane
 ```5 . 5 5 5 1 1 1 4 4 3 3 3 . 2 7 4 4 3 2 2 2 7 7 7 6 6 6 6 . ```

A003 The Dog
 ```. . . . . . . . . . . 7 . . . 7 7 4 4 5 . 1 2 . . . 1 1 2 . . . . 6 2 2 5 5 . 7 4 4 3 5 . . . . . . . . . . . 6 . . . 6 6 3 3 3 ```
A004 The robot
 ``` 7 7 7 7 . . . . . 1 1 2 2 2 . . . 1 2 3 . . . 4 3 3 . . . 4 4 3 . . . 6 4 5 6 . . 5 6 6 5 5 ```
A005 The crystal
 ```7 . . 7 7 . 4 6 6 4 4 6 3 4 2 . . . 7 . . 5 5 . 1 5 6 3 3 2 . . . . . . 5 . . 1 1 . 3 2 2 ```
A006 The castle 1 by Piet
 ```6 . . . 5 6 3 3 3 5 . . . . . 6 6 3 5 5 . . . . . 4 4 2 2 2 . . . . . 7 4 4 1 2 7 . . . 7 7 1 1 ```
A007 The bed
 ```7 . . . . . 6 7 7 3 3 3 6 6 5 . . . . . 1 7 4 4 3 2 6 1 5 . . . . . 1 5 5 4 4 2 2 2 ```
A008 The tower (Try to leave out 1 block to make it 1 story smaller. (No 6))
 ```6 6 2 2 4 2 4 2 5 5 1 1 7 1 6 . 6 3 3 3 4 3 4 5 7 5 7 7 ```

A009 The chair
 ```3 2 2 3 3 2 3 4 2 7 4 4 7 7 4 . . . . . . . . . 6 6 5 7 1 1 . . . . . . . . . 6 5 5 6 5 1 ```
A010 The bathtub
 ```2 2 2 7 7 5 5 2 3 7 5 . . . 7 5 6 3 3 3 6 4 4 1 1 6 6 4 4 1 ```
A011 The castle 2
 ```6 . . . 5 6 3 3 3 5 . . . . . 6 6 3 5 5 . . . 1 4 4 . . . . . 7 1 1 4 4 7 . . . 2 7 7 2 2 2 ```
A012 The snake
 ```2 2 . . . 2 . . . 2 4 4 . 4 4 6 . . . . . . 6 6 5 6 5 5 . . . . . . 5 3 7 3 3 3 . . . . . . 7 7 1 7 1 1 ```
A013 The tunnel
 ```. 4 4 3 . . 6 . 3 . 6 6 . 3 1 . 7 4 4 . . 5 . 3 . 6 5 . 1 1 . 7 7 2 . . 7 . 2 . 5 5 . 2 2 ```
A014 The gallow
 ```. . . . . . . . . . . . 1 7 5 1 5 5 . 2 . . 2 . . 2 . . 7 . 7 7 5 1 6 6 . 2 . . . . . . . . 4 . 4 4 6 4 3 6 . . . . 3 3 . . . . . 3 ```

A015 The cornerstone
 ```7 . . . . 7 7 . . . 2 5 5 . . 2 5 6 1 . 4 6 6 1 1 . . 7 . 2 . 4 5 4 6 . . 2 4 3 . . . 3 3 . . . . 3 ```
A016 The sofa
 ```3 3 3 4 4 2 3 4 4 6 2 2 2 6 6 . . . . . 7 . . . 5 7 7 1 6 5 . . . . . . . . . . 7 1 1 5 5 ```
A017 The steamer
 ```. . . . . . 6 6 1 . . . . . 6 7 . 5 6 1 1 . . 7 . . . 5 7 7 . 5 5 3 3 3 . . . . . 4 4 . 4 4 3 2 . . . . . . 2 2 2 ```
A018 The well
 ```1 2 2 1 6 2 6 6 2 1 . 7 3 . 5 6 . 5 3 7 7 3 4 7 3 5 5 . 4 4 . . 4 ```
A019 The monument
 ```2 . . . . 2 . . . . 2 3 5 1 . 3 3 3 1 1 . . . . . . . . 2 6 5 . 6 6 5 5 . . . . . . 4 7 . 6 7 7 . . . . 4 . 4 7 . . . 4 ```
A020 The tomb
 ```. 3 . 3 3 3 . 2 . . 2 . 7 2 1 7 7 1 . . . . . . . . . . . . 5 2 1 7 6 6 . . . . . . . . . . . . 5 4 6 5 5 6 . . . . 4 4 . . . . . 4 ```