[QUOTE=Chris Card;192320]The "smallest" (for some definition of smallest) moves that are possible are:
- flip two edges (takes 16 moves)
- rotate two corners (14 moves I think)
Chris[/QUOTE]You forgot turn one centre half a turn or two centers a quarter turn.

Jacob

[QUOTE=davieddy;192319]You were right, and the "something" you mentioned is usually called "parity".[/QUOTE]
That's probably what I meant but this was about 1981 so I wouldn't have been familiar with that word.
An interesting sidenote. ("Let's not prejudge it." - Paul Merton. What a great line.)
The first (ab)usage of that word I would have come across would be a year or two later when I bought a text adventure game:

"You are stuck in a large field of maize. All exits look the same. There is a parrot here."
Go north.
"You are stuck in a large field of maize. All exits look the same. Parrotty error. He must me pining for the fjords."

The jokes/references were lost on me at the time.

Minor notice: [URL="http://www.cube20.org"]God's number is 20[/URL].

[QUOTE=ckdo;224945]Minor notice: [URL="http://www.cube20.org"]God's number is 20[/URL].[/QUOTE]

Interesting though that the attached video is labelled 20 moves but if you count along you see 22 moves.

[QUOTE=petrw1;224964]Interesting though that the attached video is labelled 20 moves but if you count along you see 22 moves.[/QUOTE]

I think they're counting half-turns as one move, not two. Does that make up for the discrepancy?

[quote=CRGreathouse;224966]I think they're counting half-turns as one move, not two. Does that make up for the discrepancy?[/quote]
I think so.
You can single step it.

I note that none of the 20 moves consists of
a rotation of the middle layer. Would such a rotation
count as one move or two?

David

[QUOTE=CRGreathouse;224966]I think they're counting half-turns as one move, not two. Does that make up for the discrepancy?[/QUOTE]

There are 20 moves in which a face is rotated a quarter turn and 2 moves of a half turn.

[QUOTE=davieddy;224975]I note that none of the 20 moves consists of a rotation of the middle layer. Would such a rotation count as one move or two ?[/QUOTE]If the center cube is fixed, you need two moves from opposite sides to execute a middle layer rotation. Another way to see it : for a middle layer rotation you must fix two different sides and turn the remaining layer, for any other type of move you fix one part and turn the remaining layer.

Jacob

[QUOTE=S485122;225025]If the center cube is fixed, you need two moves from opposite sides to execute a middle layer rotation. Another way to see it : for a middle layer rotation you must fix two different sides and turn the remaining layer, for any other type of move you fix one part and turn the remaining layer.

Jacob[/QUOTE]

Yes that happens twice (at the middle and at the end) so that would account for the two extra move so we are back to exactly 20.

[quote=petrw1;225071]Yes that happens twice (at the middle and at the end) so that would account for the two extra move so we are back to exactly 20.[/quote]
I surmize you are referring to the top video (superflip). I think
Jacob was trying to say that a "middle layer" rotation counted as two moves, so this does not resolve your initial "22 move" observation.

If you read down to the bottom (recommended) you will
find a video of their "hardest" 20 move position.
This video is 20 moves, but the last two moves are U2D2 and
if you count this as one move, the count is down to 19.

David

BTW at least those videos avoid RSI :)

17x17x17
 

[url=http://www.shapeways.com/blog/archives/727-Oskar-van-Deventer-Produces-His-17x17x17-and-breaks-unofficial-World-Record!!.html]A world-record 17x17x17 Rubik's Cube[/url]