The mathematically inclined may be interested to know that the number of possible states for the 4D cube is exactlywhich can also be expressed as (24!x32!)/2 x 16!/2 x 2^23 x (3!)^31 x 3 x(4!/2)^15 x 4
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 43 252 003 274 489 856 000 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.
Roice wrote a paper describing many of the above puzzles and the way they exploaded from the original Rubik's cube. It was accepted as the cover article in the April 2018 edition of the journal Math Horizons.
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