Bedlam / Crazee Cube Solved
ALL 19,186 Solutions

Every possible solution to this wonderful and popular 4x4x4 cube puzzle is given below!
[ Tetris Cube SOLVED | Bedlam Cube SOLVED | Big Brother Cube SOLVED ]
[ Super IQ Cube SOLVED | Soma Cube SOLVED | Steinhaus Cube SOLVED ]

This page is for puzzle nuts, math and computing whizzes, and the truly despondent in need of a way to put the Bedlam / Crazee Cube back into its box.  If you want to solve it without help do not read any further!

My software determined the solutions using a rigorous exhaustive combinatorial search similar to the one used to originally enumerate the 19186 figure printed on the product package.  Complete details, including downloads of the entire solutions catalog and my software program and source code, are below.


Vast Search Space

The Bedlam / Crazee cube is composed of a subset of the possible 3-D pieces derived from the twelve 2-D pentominos, each having 5 cubes, plus a single 4-cube piece.  Of the 13 puzzle pieces, 7 may be rotated into 24 possible orientations, 5 may be rotated into 12 possible orientations, and 1 may be rotated into 3 possible orientations.  This means there are 247 x 125 x 31 =  3,423,782,572,130,304 (over 3 quadrillion) possible piece orientation combinations to try. The pieces may also be fitted, or 'tiled', into the 4x4x4 cube in 13! = 13x12x11x(...)x2x1 =  6,227,020,800 possible piece ordering permutations. The product of these numbers is 42,639,930,582,665,806,636,646,400 (over 42 million quadrillion, or over 42 billion trillion) steps to try every possible orientation of every possible piece order permutation!

Because the cube is a rather snug 4x4x4 box there are many piece orientations that simply will not fit into the box with other pieces in their own various orientations, as anyone who tries to manually assemble a Bedlam cube knows from personal experience!  Consequently, the number of permutations and therefore the number of piece orientations to attempt to tile into the box are drastically diminished.  For example, the initial piece order is 0,1,2,3,4,5,6,7,8,9,10,11,12.  The next is 1,0,2,3,4,5,6,7,8,9,10,11,12 and then 2,0,1,3,4,5,6,7,8,9,10,11,12 etc.  When the permutations are fully exhausted the piece order is, finally, 12,11,10,9,8,7,6,5,4,3,2,1,0.  For the initial permutation, say pieces 0 and 1 are already in the box but none of the orientations for piece 2 fit. For this example, that would indicate 13!/(13-11)! = 3,113,510,400 permutations are immediately eliminated from having to be attempted, multiplied by the number of possible orientations for each of those pieces in all those discarded orientations. This can happen at any stage of the search, so the search space is in practice vastly smaller than the 42 million quadrillion figure above, bringing it into reach of a software program.

Of the 6,227,020,800 possible piece ordering permutations only 460,464 produce a completed cube (see below, Search Results). This means you have about 1 chance in 13,523 that a random lineup of the pieces can be put into a cube.  No wonder it's not so easy! The Bedlam cube is therefore about 6.7 times harder than the Tetris cube, for which you have about 1 chance in 2,028.

Search Algorithm

Each of the 13 pieces is arbitrarily assigned a unique number, 0 to 12 (diagram below). The software encodes the 3-dimensional coordinates of each cube of each piece, and then rotates them in 4 possible positions around each of the 3 axes (x,y,z) to generate every possible unique orientation and build a quick reference lookup table.  The piece order permutation order is initialized to 0,1,2,3,4,5,6,7,8,9,10,11,12 and the orientations of each piece are reset.  A 4x4x4 3-dimensional box is encoded and the initial empty cube is scanned starting at (x,y,z) coordinates (1,1,1).

The first orientation of the first piece in the permutation is fitted (or not) into the box. If it doesn't fit, the next orientation is tried, etc. If the piece fits, the next empty cube in the box is scanned along the x-axis, then y-axis, then z-axis. If the next empty cube is isolated, the last piece orientation fitted into the box is removed and its remaining orientations are tried. If the next empty cube is not isolated, the next piece in the permutation order is attempted the same way.  If none of the orientations of a piece fit into the box without isolating the next empty cube, the piece order permutation is advanced so the next piece in the ordering becomes the next piece to try, and it's first orientation is attempted, etc.

By repeating this process, literally every possible orientation of every possible ordering of pieces is visited by my search software program, an undeniably rigorous method. This method will produce multiple rotated copies of each unique solution, so a further step in the program spins the solved cube around each axis and compares each rotation with a catalog of saved solutions.  Only new unique solutions are then added to the catalog as the permutation sequence progresses, guaranteeing the correct catalog is produced.

  Diagram of the 13 Bedlam/Crazee Cube pieces
and the arbitrary numbers 0 to 12 assigned to each in the software program and solutions catalog.

Pieces 0 to 9 are labeled by their own numbers but 10, 11 and 12 are labeled A, B and C, respectively, in the solutions catalog.

Piece 0 has 5 cubes, labeled blue 'flat-R'
Piece 1 has 5 cubes, labeled red 'flat-X-plus'
Piece 2 has 5 cubes, labeled yellow 'flat-W'
Piece 3 has 5 cubes, labeled red 'bent-W-tip'
Piece 4 has 5 cubes, labeled yellow 'folded-X'
Piece 5 has 5 cubes, labeled red 'z-bump'
Piece 6 has 5 cubes, labeled yellow 'bent-T'
Piece 7 has 5 cubes, labeled red 'tall-L-bump'
Piece 8 has 5 cubes, labeled yellow 'twisted-Z'
Piece 9 has 5 cubes, labeled yellow 'L-bump-end'
Piece 10 has 5 cubes, labeled blue 'squiggle'
Piece 11 has 5 cubes, labeled blue 'bent-R-tip'
Piece 12 has 4 cubes, labeled yellow 'squiggle'

Search Results

Exactly 19,186 unique solutions were found. Because of rotational symmetry my software actually assembled 24 x 19,186 = 460,464 cube solutions but it discarded exactly 441,278 duplicates as 23 additional rotational copies of each unique solution.  The software search completed in 86 hours on my old 2 GHz Pentium 4 laptop. The 19,186 unique solutions, however, were found within the first 30 hours and the remaining 56 hours completed permutations that resulted in rotational copies. The search space was, as expected, enormously reduced to a 'mere' total of exactly 166,604,324,836 (166.6 billion) piece order permutations visited, including dead-end orientation paths.  The program attempted to fit pieces into the box exactly 2,407,717,843,902 (2.4 trillion) times and succeeded fitting them exactly 66,924,356,081 (66.9 billion) times. Indeed, 2.4 trillion is MUCH smaller than 42 million quadrillion!

Bedlam / Crazee Cube Solutions

Below is the software's startup analysis, the first 3 of the entire solutions catalog, and the search conclusion outputs, rigorously determined using 'brute-force' combinatorial techniques (color added for web page annotation).  Pieces are mapped to numbers 0-12 and their identification is aided by the descriptive cube counts, colors and labeling in agreement with the diagram above.  The solutions are given in layers of the 4x4x4 box, with the top layer of the cube on the left and ending with the bottom layer on the right.  Pieces 0 to 9 are given in the solutions by those numbers, and pieces 10, 11 and 12 are given as A, B, and C respectively.

It takes a bit of visualization to see the pieces in the printed solutions and it helps to refer to the diagram above. In Solution 1 below piece 1 is outlined, resting entirely in the bottom cube layer. Particularly challenging to visualize are pieces spanning cube layers, such as piece B (blue 'bent-R-tip'), which in the outlined example in Solution 1 has the 'bent-tip' on the end of the 'R' in the third layer next to the A cubes, and two cubes going up into the second layer, and finally a single cube in the (leftmost) top layer.  Get out your Bedlam cube and try it... it's rather easy once you get the hang of it.

Bedlam Cube Solver, (c)2008 www.scottkurowski.com

Piece 0 has 5 cubes, labeled blue 'flat-R'
Piece 1 has 5 cubes, labeled red 'flat-X-plus'
Piece 2 has 5 cubes, labeled yellow 'flat-W'
Piece 3 has 5 cubes, labeled red 'bent-W-tip'
Piece 4 has 5 cubes, labeled yellow 'folded-X'
Piece 5 has 5 cubes, labeled red 'z-bump'
Piece 6 has 5 cubes, labeled yellow 'bent-T'
Piece 7 has 5 cubes, labeled red 'tall-L-bump'
Piece 8 has 5 cubes, labeled yellow 'twisted-Z'
Piece 9 has 5 cubes, labeled yellow 'L-bump-end'
Piece 10 has 5 cubes, labeled blue 'squiggle'
Piece 11 has 5 cubes, labeled blue 'bent-R-tip'
Piece 12 has 4 cubes, labeled yellow 'squiggle'

Piece 0 has 24 unique rotational orientations
Piece 1 has 3 unique rotational orientations
Piece 2 has 12 unique rotational orientations
Piece 3 has 24 unique rotational orientations
Piece 4 has 12 unique rotational orientations
Piece 5 has 24 unique rotational orientations
Piece 6 has 24 unique rotational orientations
Piece 7 has 24 unique rotational orientations
Piece 8 has 12 unique rotational orientations
Piece 9 has 24 unique rotational orientations
Piece 10 has 12 unique rotational orientations
Piece 11 has 24 unique rotational orientations


[ NOTE: The remaining 19,183 solutions are omitted here.
To download the full catalog click BedlamCubeSolved.zip ]
All permutations exhausted, 19186 unique solutions found, 441278 duplicate rotations discarded
Total permutations = 166604324836, tiles attempted = 2407717843902, tiles succeeded = 66924356081
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Bedlam / Crazee Cube Solver Software

Download the program bedlamcube.exe, a simple console application without buttons or windowing and its 700 lines of C language source code file bedlamcube.c, in BedlamCubeSolved.zip. Run it yourself!  Every 1,000,000 piece order permutations are output to the console screen.  Email me at the address at the bottom of the page and tell me the kind of computer you used and how long it took to run.  This code was originally written to solve all 9,839 solutions of the Tetris cube and with a few trivial tweaks determined all 480 unique solutions of Piet Hein's Soma cube puzzle in 10 seconds (note: this linked reference cites only 240 unique solutions), both unique solutions of Hugo Steinhaus' cube in 1 second,  all 14,177 solutions of the Brother Cube, and would work for other 3D box-tiling puzzles.  Note there are copyright restrictions given in the bedlamcube.c source module and readme.txt files to observe regarding modification of the source code and/or re-publishing the code or output data file.

Background and Credits

I owe this particular puzzle-solving adventure to my son Dylan, who recently challenged me to find 'even one [Tetris Cube] solution, daddy!' and witnessed my struggle to manually restore his Tetris Cube to its plastic box.  I told him there was a way to use a computer to find every possible solution, so we encoded the cube coordinate positions of the 12 Tetris cube pieces on paper, and I later put that into this software over the span of a handful of days.  Thank you, Dylan!

In 1986 I wrote a software program to exhaustively solve and catalog all solutions of the 2-dimensional pentomino puzzle, to the later delight of Stanford Professor Emeritus Donald Knuth, which has tens of thousands of solutions in various box dimensions (3x20, 4x15, 5x12, 6x10 and 8x8 with several 2x2 hole positions) even after sifting out reflected and rotated copies.  I also have over a decade of experience creating  and running  supercomputer-capacity  research projects so I was fully prepared to organize any "heavy duty processing power" required to catalog all the solutions and verify their number as claimed by the Tetris Cube's creators, but a laptop computer was enough.

Contact me at

Last updated January 14, 2009