On: Show HN: Scroll through all 43252003274489856000 Rubik's Cube states

[theginger]

Anyone else surprised how small the number is? It looks quite big without commas but if you add them in it looks like the sort of number that is almost conceivable 43,252,003,274,489,856,000 43 quintillion, that's the type of number i've vaguely heard of. Compared to the number of possibilities for a shuffled deck of cards 80,658,175,170,943,878,571,660,636,856,403,766,975,289,505,440,883,277,804,000,000,000,000 Thats a big number, and weirdly I think those 00s at the end are exact not a rounding error.

[xboxnolifes → theginger]

It felt pretty big to me, considering Rubik's cubes only have 26 pieces, their valid slots are not all the same, and some of their states are mirrored.

[BurningFrog → xboxnolifes]

It's really 21, since the centers are all one unmovable piece.

https://jhodileongseportfolio.weebly.com/center-faces.html

[xboxnolifes → BurningFrog]

Good catch, forgot about that.

[onraglanroad → theginger]

The number of permutations is 52! which is 1x2x3...x51x52

So, at some point you're going to be multiplying by 10, 20, 30 etc. Plus you'll have 2x5x.., 4x50x... (if you rearrange the terms). It therefore makes sense that you'll end up with a bunch of zeros on the end.

[onraglanroad → onraglanroad]

In fact that means the largest factorial that doesn't end in 0 must be 4! because you could always move the ...x2x5 to the end of the series.

[BurningFrog → theginger]

And yet sorting a deck of cards is much easier than solving the cube.

43,252,003,274,489,856,000 is a fun trivia number, but it tells you nothing about how hard it is to solve the cube.

[Polizeiposaune → BurningFrog]

Current speed cube record appears to be 2.76s.

Has anyone ever sorted a randomly shuffled deck of cards in under 3 seconds?