A SOMA challenge: The number 7 piece can occupy 4 positions in the cube (not counting rotations
and reflections). Construct the SOMA Cube with the 7 piece in each of the following positions:

Bury the 7

A SOMA Challenge: Construct the "Buried 7" solution of SOMA cube, shown at the
right, where the number 7 piece is
placed so that it's central cube is at the center of the SOMA cube. Only the three outward faces of
its three arms are visible (shown in yellow). Of course, more than one solution may be
possible.

The Balancing Soma Cube

This interesting information about the Soma Cube was published in Martin Gardner's Mathematical Games column
in July, 1969.

Martin Gardner notes in the article that there are 240 different ways the cube can be formed
not counting rotations and reflections as being different. This figure was established in 1962 by
John Conway and M.J.T. Guy, who were mathematicians at the University of Cambridge. In analyzing
his work, Conway discovered the curious fact that only one of the 240 solutions allows the
Soma cube to be balanced on a pedistal that touches only the central square of the cube's 3 by
3 unit base. This solution is diagrammed below. The central square of the bottom layer is the
one that rests on the pedistal.

TOP

MIDDLE

BOTTOM

6

7

7

6

6

7

3

1

1

5

5

7

3

6

4

3

1

4

5

2

4

5

2

4

3

2

2

Addendum:
The following additional solution to the balancing cube has been produced by Stuart Collins of
Nottingham, UK in June, 1998 and refutes Conway's uniqueness assertion stated above!

Are there more solutions
to this problem? Mr. Collins conjectures that any of the flat 4-cube pieces ( 2,3, and 4 ) might
serve as the balance piece. It only remains to be shown that the 3 piece can serve this function.

TOP

MIDDLE

BOTTOM

2

2

1

7

1

1

7

7

3

2

6

6

5

5

3

7

5

3

2

4

6

4

4

6

4

5

3

Piece Duplication

Doubling each dimension of any piece will multiply the volume by 8. For any of the
pieces comprised of 4 unit cubes, this increases the volume from 4 cubic units to 32 cubic units.
For piece number 1, the volume increases from 3 cubic units to 24 cubic units. This equals the
total number of unit cubes in the remaining 6 pieces. This poses a possible problem: Can you construct a figure
similar to the number 1 piece but with all dimensions doubled, using the remaining 6 Soma
pieces? The answer is yes, and the challenge is to construct this figure.

Solutions for selected figures in the Soma Gallery

I am including a few illustrations of how to solve these figures. The viewer is urged to
make every effort to solve these figures without consulting these solutions. They can all be done
if you work at it for awhile. You certainly get more satisfaction if you discover the solution
yourself. Then, once you solve it, you may wish to compare your solution with mine.

These figures have graphics showing the solutions: