Magic Cube 4D


MagicCube4D is a fully functional four-dimensional analog of Rubik's cube plus
dozens of beautiful new 4D puzzles besides just the hypercube . The image above shows the 34 puzzle in its solved state. Click on it for a simple resizable applet version that you can interact with to get a feeling for how it works. Then download the full-featured application below and try to solve it.

or right click here and select "Save Link as"

The program is packaged in an executable jar file which should run on any system with a Java virtual machine installed. Save it to your desktop or anywhere you like, so long as you can find it later. Simply double click it to launch. Please read the FAQ for a more complete description of the puzzle. The Java applet or application should run on any machine, but if either one fails to start you probably just need to install a current Java virtual machine. Click here for the latest version.

Don Hatch and Melinda Green have developed this puzzle on and off starting in 1988. Jay Berkenbilt and Roice Nelson later joined and made major contributions. Don and Jay were the first to have solved the puzzle making extensive use of macros. Roice was the first person to solve the puzzle without using macros. For his solution he extended Philip Marshall's 3D  "Ultimate Solution to Rubik's Cube" into 4D. You can learn Roice's solution if you don't feel like trying to solve it yourself first.

Project Pages

Want to learn more or get involved? The following quick links will tap you straight in.

Nerd Notes

The mathematically inclined may be interested to know that the number of possible states for the 4D cube is exactly

 (24!x32!)/2 x 16!/2 x 2^23 x (3!)^31 x 3 x(4!/2)^15 x 4

which can also be expressed as
32! 24! 16! 2^22 6^32 12^15
or in decimal as
1 756 772 880 709 135 843 168 526

079 081 025 059 614 484 630 149

557 651 477 156 021 733 236 798

970 168 550 600 274 887 650 082

354 207 129 600 000 000 000 000

For comparison, the normal 3D Rubik's Cube has only43 252 003 274 489 856 000 unique positions which is still huge. On the other hand, the 4D cube has more potential positions than the total number of atoms in the universe! Far more. Talk about a needle in a cosmic haystack! Click the following link to learn how to calculate 4D cube permutations. Surprisingly, even though the number of 4D cube positions is frighteningly large this doesn't mean this puzzle is that many times harder to solve. If you can already solve the 3D cube, then you're more than half way to solving this one. All the techniques you already know will apply here as well.

Related Puzzles

We hope you enjoy our puzzles and would love your feedback. We only require that if you want to use it for some commercial purpose such as adding it to a game pack, or using it as a demo to help sell your product, that you get our written approval first.

Programmers are free to use and modify the code for non-commercial purposes as long as obvious credit for the source of the code and the designs it embodies are clearly made, and ports and derived versions of 4D Magic Cube programs are not distributed without the express written permission of the authors.
Other 4D Cube Puzzle Implementations
Web Pages Linking to this one (found using Google link look-up)

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