2x2x2x2¶
2x2x2x2
Shape: Tesseract
Pieces: 16
History¶
The 2x2x2x2 (normally referred to as the 24) is a 4-dimensional twisty puzzle in the shape of a hypercube that is cut in half on each of the 4 axes.
The first official 24 solve on the Hall of Fame was done by Jay Berkenbilt in 2004 using MC4D, although it was probably solved several times before that.
Permutations¶
The 16 4cs of the 2x2x2x2 can be placed in any even permutation. In order to identify positions that are a whole-puzzle rotation apart from each other, we fix one 4c, leaving 15 4cs that can be permuted. Each 4c can be placed in \(\frac{4!}{2}\) orientations, except the last, which can be placed in only \(4\) orientations. Thus, the number of permutations of the puzzle is \(\frac{15!}{2} \cdot \left(\frac{4!}{2}\right)^{14} \cdot 4 \approx 3.36 \cdot 10^{27}.\)
Physical version¶
Since 2013, Melinda Green has been refining her physical 2x2x2x2. See her project home page for more details.