Soma Cube Solver
How to use the Soma cube solver
Choose the cube or one of the figures. Press Next piece and the solver lays down one piece at a time, in an order you can follow with the real set: every piece rests on the table or on pieces already in place, and nothing sits above it, so it can be lowered straight in. The piece you have just placed is shown on its own beside the build, with its letter, so you can pick the same one out of the box.
Turn it rotates the whole thing a quarter turn, to see the side that faces away. Another solution starts again with a different answer.
How many solutions does the Soma cube have?
240. That is the usual figure, and it counts an answer and its mirror image as one, and treats the cube turned round as the same cube. Counted more literally there are 11,520 ways to fill a 3 by 3 by 3 box with the seven pieces: dividing by the 24 ways to turn a cube gives 480, and counting mirror images as one halves that to 240.
The numbers on this page were worked out, not copied. Two separate programs counted every figure and agree on all of them.
The seven pieces
Every Soma piece is made of unit cubes, and between them they are every irregular shape you can make from three or four cubes. V is the only one with three. L, T and Z are flat. A and B are mirror images of each other, the same twist turned opposite ways, so they look alike and never swap places. P is a corner cube with one more cube in each of the three directions. Three of the seven do not lie flat, which is why no flat shape can be built from the full set.
Beyond the cube
The same seven pieces build a long list of other figures, and the count tells you how hard each one is: fewer solutions means fewer arrangements to stumble into. Of the figures here the Zigzag is the hardest, with 48, and the L Block the most forgiving, with 3,069. The Soma cube shapes page has the same figures as printable challenge sheets.
More on the Soma cube
Where it came from, the mathematics inside it, and why 240 solutions still leaves it hard are all in the Soma cube explained. We make Soma puzzles of our own: Soma Flop, Shrinking Soma and Ochinai Soma, with the rest in Soma cube puzzles. For pieces of your own in a box of your own, use the packing puzzle solver.
Frequently Asked Questions
How do you solve a Soma cube?
Lay the pieces in an order where each one rests on the table or on pieces already down. There are 240 solutions, so there is no single sequence to learn; this solver shows one of them a piece at a time, and the next button gives you another.
How many solutions does the Soma cube have?
240, counting an answer and its mirror image as one and the cube turned round as the same cube. Literally there are 11,520 ways to fill the box: 480 once turning is ignored, 240 once mirror images are too.
What are the seven Soma cube pieces?
Every irregular shape you can make from three or four cubes: V, the only three-cube piece; L, T and Z, which are flat; A and B, mirror images of each other; and P, a corner cube with one more cube in each direction.
What shapes can you make with a Soma cube?
A long list beyond the cube. The solver has eleven of them, from the Zigzag, the hardest with 48 solutions, to the L Block, with 3,069. No flat shape is possible, because three of the seven pieces do not lie flat.