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SOMA Cube

Infosheet

Puzzle type: Put together, shape assembly, solid dissection
Skills involved: visual perception, spatial reasoning, logical reasoning

Difficulty level: 3/10
Time taken: 10 min
Suitable age: 3+

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Objective

Assemble the seven shapes into a 3x3x3 cube. How many solutions can you find?

History & Trivia

This puzzle was invented by Danish poet and writer Piet Hein in 1933 during a lecture on
quantum mechanics conducted by Werner Heisenberg.

The pieces of the Soma cube consist of all possible combinations of three or four unit
cubes, joined at their faces, such that at least one bend is formed. In other words, they are
all the possible shapes that can be made with 3 or 4 identical cubelets, that are not
rectangular.

Soma is a Sanskrit word for a euphoric plant extraction, used in ancient India as a narcotic.
Soma is also referenced in Aldous Huxley’s Brave New World.

The Soma cube has 240 unique solutions. If you find that impressive, the 4x4x4 version of
this puzzle known as the Bedlam cube has 19,186 distinct solutions!

Hints & Tips

#1: Use the bigger odd-shaped pieces first and save the 3-unit ‘v’ piece for the last.

#2: In all solutions to the puzzle, there is only one kind of position which the ‘T’ piece can
take. The ‘T’ piece always occupies two corners in a solution. One can compare the number
of corners of the whole cube and individual pieces to arrive at this conclusion.

#3: The ‘L’ piece must at least form one corner and its cubelets cannot take the central spot.
Can you figure out why?

Extension

The same pieces can be used to form a large variety of other appealing 3D shapes,
including dogs, chairs and skyscrapers, easily found on the internet. Better still, invent your
own shapes! Can you analytically find a shape that is impossible to make with the pieces?

Try your hand at making your own Soma Cube with wooden blocks!

If you liked this puzzle, try the Domino Dice Cube or Conway’s Packing Box next.

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