The Soma Cube: 240 Solutions and the Ones That Are Harder
The Soma Cube: 240 Solutions and the Ones That Are Harder
Seven pieces. Twenty-seven cubes. One 3x3x3 box of space to put them in.
It is the most copied puzzle design of the twentieth century, the cube alone has 240 different correct answers, and people still cannot do it. Those two facts are related, and not in the way you would expect.
Watch: Seven Pieces, One Cube
One minute, one solution out of the 240. If you would rather find your own, skip it - the rest of this page explains how the puzzle works without giving an arrangement away.
What the Soma Cube Is
The set is defined by a rule rather than chosen by taste, which is part of why it has lasted.
Take every way of gluing three or four unit cubes together face to face, then throw out any that come out straight or flat. What you have left - every small block with at least one inside corner - is exactly seven shapes. One of them is made of three cubes, the other six are made of four.
Three plus twenty-four is twenty-seven, which is a 3x3x3 cube exactly. That is not a coincidence the designer engineered afterwards. It falls out of the rule, and that is the elegance people have been repeating for ninety years.
Where It Came From
It was invented by Piet Hein, a Danish polymath, in 1933. He worked it out during a lecture on quantum mechanics given by Werner Heisenberg.
The story gets told as a joke about a bored student, but the detail worth keeping is what he was listening to. Heisenberg was describing how space gets carved up, and Hein started wondering how many irregular pieces you would need to fill a cube. He had the answer before the lecture ended.
The 240 Solutions, and the One That Stands Alone
There are 240 distinct ways to build the 3x3x3 cube, once you stop counting rotations and mirror images as different.
John Conway and Michael Guy found all 240 by hand in 1961, with no computer, and then did something better than counting them. They drew a map. Two solutions were joined if you could get from one to the other by pulling out two pieces, twisting them, and putting them back. The result - they called it the Somap - has 240 points on it, and 239 of them are connected to each other.
One solution is an island. There is no pair of pieces you can twist to reach it from anywhere else. If you find that one, you found it on its own.
Why 240 Answers Does Not Make It Easy
You would think 240 correct answers would make a puzzle generous. In practice it does the opposite, and for a reason that is worth understanding before you buy any version of it.
Having many solutions means no single move is ever clearly wrong. On a puzzle with one answer you get feedback constantly - a piece does not fit, so that branch is dead, back up. On the Soma cube almost any pair of pieces will sit together happily. You can be four pieces in, entirely comfortable, and already in a position that cannot be finished. The failure arrives at the end, with two pieces left and a hole of the wrong shape, and it tells you nothing about which of your earlier choices was the bad one.
And the cube is only one target. The same seven pieces build a great many other shapes - towers, stairs, walls, chairs, animals - and this is the part people miss: every shape is a different puzzle. Its own solution path, its own dead ends, its own moment where the last two pieces do not fit. Solving the cube teaches you remarkably little about building the next shape. So the real size of the Soma set is not 240 answers to one question. It is a new question every time you choose a new shape.
That is what Cube Alchemy is built around. Greg went through the possibilities, picked his 180 favourites and compiled them into one booklet, so the 3x3x3 cube is challenge one of a hundred and eighty rather than the whole puzzle.
Same Seven Pieces, New Rule
Because the piece set is fixed and famous, designers use it the way musicians use a standard: everyone knows the tune, so the interest is in what you do to it. Three of the puzzles we carry take the identical seven pieces and add a single constraint, and each one makes the familiar set behave like something you have never handled.
Ochinai Soma adds gravity. Designed by Hiroshi Fujino, it gives you a box with a hole cut through the base. Packing the pieces in is only half of it - the puzzle is solved when you turn the whole thing over and nothing falls out. The pieces have to hold each other up across the gap. Ochinai means roughly will not fall in Japanese, and the set contains two boxes, so it is two puzzles rather than one.
Soma Flop changes the door. A Dr Volker Latussek design, where the opening in the box will not accept pieces the sensible way up. You are no longer working out where each piece goes so much as what attitude it has to be in at the moment it crosses the boundary.
Shrinking Soma removes the slack. Also Latussek, and the strictest of the three. The space is 4x4x4, the opening is restricted, and the puzzle is not finished when everything is inside - it is finished when nothing can move. Shake it and it stays put. Knowing the 240 standard solutions helps almost not at all here, which is the joke built into it.
There is a fuller account of how Latussek builds that kind of difficulty in our profile of his work.
The format attracts this treatment from everyone. Allard Walker wrote about a version called Broken Soma - not one we carry - which splits the small three-cube piece up and distributes the fragments among the others. His verdict was thoroughly evil, and he admitted to enjoying watching experienced solvers struggle with it for months.
Frequently Asked Questions
How many pieces does a Soma Cube have?
Seven, made of twenty-seven unit cubes in total. One piece is three cubes and the other six are four cubes each. The seven are not an arbitrary selection - they are every possible shape you can make from three or four cubes that is not straight or flat.
How many solutions does the Soma Cube have?
240, counting rotations and mirror images of the same arrangement as one solution. Conway and Guy enumerated them by hand in 1961. If you count every rotation and reflection separately the number is far larger, which is why you will sometimes see 11,520 quoted instead.
Who invented the Soma Cube?
Piet Hein, in 1933. He was a Danish polymath - poet, designer and mathematician - and he came up with it while sitting in a lecture on quantum mechanics given by Werner Heisenberg.
Is the Soma Cube hard if there are 240 solutions?
Yes, and partly because of them. Many solutions means almost no arrangement feels wrong while you are building it, so you get no warning that you have gone astray until the last two pieces will not go. A puzzle with a single answer pushes back much sooner.
What can you build with a Soma Cube besides the cube?
A great many shapes - towers, chairs, stairs, animals, walls. The seven pieces are a general-purpose set and the 3x3x3 cube is only the best known target. Cube Alchemy comes with a booklet of 180 shapes chosen by Greg, so the cube is the first challenge rather than the whole puzzle.
Are all Soma Cube puzzles made from the same seven pieces?
Yes. The seven-piece set is standard and every puzzle here uses it unchanged - what the designers alter is the box and the rule. That is why you can own several without them feeling repetitive, and why the constrained versions assume you already recognise the pieces on sight.
What Soma Cube Puzzle Should You Get?
If you are new to this, go with Cube Alchemy. It is the standard seven-piece set, and because the booklet keeps handing you new shapes it does not stop being useful after the first success.
If the plain cube is behind you, Ochinai Soma is the most enjoyable next step - the upside-down test is a genuinely new sensation and there are two boxes in the set.
If you want the hard end, take Soma Flop before Shrinking Soma. Both are Expert, but Flop is built on one clear idea you can keep in your head.
All four sit in the Soma cube puzzles collection. The constrained versions are packing puzzles at heart, so if that side appeals, our guide to packing puzzles covers the wider family, and everything else lives in the mechanical puzzles collection.