Cl1mh4224rd

2006-Jun-04, 06:44 PM

...here's a couple variations to break your brain on.

MagicCube4D (http://www.superliminal.com/cube/cube.htm):

MagicCube4D is a fully functional four-dimensional analog of Rubik's cube. [...]

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 only 432 520 032 274 489 856 000 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.

If that wasn't evil enough...

MagicCube5D (http://www.gravitation3d.com/magiccube5d/): A 5-dimensional version of the above.

MagicCube4D (http://www.superliminal.com/cube/cube.htm):

MagicCube4D is a fully functional four-dimensional analog of Rubik's cube. [...]

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 only 432 520 032 274 489 856 000 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.

If that wasn't evil enough...

MagicCube5D (http://www.gravitation3d.com/magiccube5d/): A 5-dimensional version of the above.