# 2x2x2x2¶

## History¶

The 2x2x2x2 (normally referred to as the 2^{4}) 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 2^{4} 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.