The Bedlam Cube: 19,186 Solutions, Still Brutal

Quick answer: the Bedlam Cube is a 4x4x4 assembly puzzle of 13 polycube pieces, twelve pentacubes and one tetracube, invented by Bruce Bedlam and sold since 2005. It has 19,186 distinct solutions up to rotation and reflection, and is nonetheless much harder than a Soma cube, which has 240.

Best for: people who have solved a Soma cube and want the version that does not forgive anything.

Nineteen thousand answers sounds like a puzzle that practically solves itself. It is the single most misleading number in puzzle marketing.

What Is the Bedlam Cube?

Thirteen pieces built from unit cubes: twelve pentacubes, each five cubes glued into a rigid shape, and one tetracube of four. Twelve fives and a four is sixty-four, which is exactly 4x4x4 with nothing to spare.

The goal is to assemble all thirteen into the cube. No piece is left over and no gap is permitted, which puts it in the assembly family described in assembly puzzles explained rather than among the interlocking ones: nothing has to be removed in a sequence, and the difficulty is entirely in which shape goes where.

Why Do 19,186 Solutions Not Make It Easy?

Because the number you want is not how many solutions exist, it is what fraction of arrangements are solutions.

Thirteen distinct pieces, each with up to 24 orientations, placed into 64 cells generates a search space so large that 19,186 is a vanishing slice of it. The ratio, not the count, is what you experience while solving. By that measure the Bedlam Cube is far more hostile than its headline number suggests.

The comparison that makes this concrete is the Soma cube: seven pieces, a 3x3x3 cube, 240 solutions. Eighty times fewer answers, and most people solve it in an evening. The Bedlam Cube has eighty times more answers and defeats people for months.

The reason is the pieces. Pentacubes are large and awkward relative to a four-wide cube, so a single misplaced piece in a corner can poison the entire remaining space. With Soma's smaller pieces there is room to recover. Here there is not, and you usually cannot tell which of your first five placements was the fatal one.

Where Did It Come From?

It was invented by the British puzzle designer Bruce Bedlam and has been sold since 2005.

Its commercial story is unusually well documented, because it went on the BBC's Dragons' Den in the 2005 series. Rachel Elnaugh and Theo Paphitis offered 100,000 pounds for a 30% equity share in Bedlam Puzzles. Danny Bamping, the entrepreneur behind the cube, turned the offer down and took a bank loan instead, which the programme revisited in a later Where Are They Now episode.

Bamping also holds the Guinness record for assembling it: 11.03 seconds, on 9 November 2006. That is a record for a known solution executed by muscle memory, not for solving it cold, and the gap between those two things is the whole character of the puzzle.

How Do You Solve the Bedlam Cube?

Assume you will not find it by fitting pieces together and hoping. The approaches that work are all about where you commit first.

Start with the corners and the awkward pieces. The most irregular pentacubes have the fewest legal positions, so place them while the cube is still mostly empty. Saving the difficult piece for last guarantees it will not fit, because by then its options are gone.

Fill a layer only if the layer can stand alone. A 4x4x4 cannot generally be split into four flat 4x4 layers, because pentacubes span layers. Attempting layer-by-layer assembly is the commonest wasted week. Think in corners and blocks rather than floors.

Watch for isolated single cells. The moment the remaining space contains a gap of one or two cells that no five-cube piece can reach, you are finished and should stop. Learning to spot a dead space three placements early is the single biggest improvement available.

Count what is left. If you have placed some pieces and the empty volume cannot be divided into shapes matching your remaining pieces, back up. Checking the remaining volume is quick; checking the remaining shapes is what actually saves time.

Keep a solved photograph. Once you find a solution, photograph it disassembled and in order. With 19,186 solutions you will not stumble on the same one twice, and there is no shame in being able to return to a cube you have already earned.

What Do Collectors Say About It?

The most honest assessment I have read comes from Gabriel Fernandes, who has written about it on his puzzle collection blog.

He calls it a simple assembly/packing puzzle, but a headache to solve, and puts the number in its place directly: You have 19,186 ways to do it. Sounds a lot, but it's very hard to work out a solution.

The detail worth repeating is what happened next. He became, by his own account, obsessed with collecting colour variations of it from eBay, building a sub-collection within his collection, while adding that he is yet to find a single solution for it. Someone who owns many Bedlam Cubes and has solved none of them tells you more about the puzzle than any difficulty rating.

Fernandes also notes an easier official version, the Bedlam Treasure Chest Cube, with only nine pieces and 37 solutions, which is the sensible entry point if the full thirteen sounds punishing.

What Should You Try Instead?

We do not make a Bedlam Cube. It is a modern commercial design rather than a public-domain classic, and the honest comparison is to the polycube puzzles we do make.

Cube Alchemy is the direct equivalent one size down: seven pieces, a 3x3x3 cube, and a booklet of 180 curated challenges beyond the cube itself. If you want the same assembly problem with packing constraints added, Cubiz is five pieces into a box where the lid must sit flush, and Four Fit is the brutal four-piece version.

The shelves are 3D assembly puzzles, Soma cube puzzles and mechanical puzzles.

Frequently Asked Questions

What is the Bedlam Cube?

A 4x4x4 assembly puzzle of thirteen polycube pieces, twelve made of five unit cubes and one of four, invented by Bruce Bedlam and commercialised from 2005. All thirteen must fill the cube exactly.

How many solutions does the Bedlam Cube have?

19,186 distinct solutions, counted up to rotations and reflections. That sounds generous but it is a vanishing fraction of the possible arrangements, which is why the puzzle is still extremely hard.

Is the Bedlam Cube harder than a Soma cube?

Considerably. The Soma cube is seven pieces into a 3x3x3 with 240 solutions and most people manage it in an evening. The Bedlam Cube's pentacubes are large relative to a four-wide cube, so one bad early placement ruins the remaining space with no way to recover.

What is the Bedlam Cube world record?

11.03 seconds, set by Danny Bamping on 9 November 2006 and recognised by Guinness World Records. That is a memorised solution executed quickly rather than a cold solve.

How do you solve the Bedlam Cube?

Place the most irregular pentacubes first, while the cube is still empty and they still have legal positions. Do not try to build flat layers, because pentacubes span them. Watch for gaps of one or two cells that no piece can fill, and back up as soon as one appears.

Was the Bedlam Cube on Dragons' Den?

Yes, in the 2005 series. Rachel Elnaugh and Theo Paphitis offered 100,000 pounds for 30% of Bedlam Puzzles, and Danny Bamping declined in favour of a bank loan.