SOMA News 01 Dec 1998 E-Mail.

## SOMA Alternatives (Checkered, Couples, Balancing)

### [Go Top]     The Checkered SOMA

The idea for the Checkered Soma was published in the first issue of The Soma Addict as an alternative way of forming the cube and other figures. This idea was created by Piet Hein himself and put down on paper on June 20, 1970. Shown below is a diagram depicting the proper placement of the checkered cubes. Try making one and see if you can build the cube for an added challenge!
This is actually an inverted "Satz-Ls" as described in News2016.09.22 How about checkered solutions having 219 cube solutions.

### [Go Top]     Couples

The following figures are known as "couples." A couple is made with just one Soma Cube, but some of the seven pieces are independent of one another as the figures stand separately. Try to make the following couples and see what other ones you can come up with.

Do note that the shape #P002 is doubling the figure size, and that the figures #P001 and #P003 can be combined to form the cube.

### [Go Top]     Piece Duplication

Above is a pair figure from the set: P0001-0025

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.

- Carefully edited by Thorleif Bundgaard.

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