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In response to Richard Pavelle's message, there are about 7.4*10^45

color combinations. See "mc:alan;cube 4x4x4" for more details on the

subject (especially the derivations) by Dan Hoey.

I bought a solution book from my favorite bookstore today. The title is

"The Winning Solution to Rubik's Revenge". It is a sequel to "A Winning

Solution to Rubik's Cube" by the same author (Minh Thai), who is billed

as the U.S. National Champion of the Rubik's Cube-A-Thon. I assume the

Revenge book is not REALLY a winning solution... at least not yet.

His method is to put all corners together, go for two opposite centers,

then the edges of said centers. Next he goes for the remaining edges

(numbering eight), and then the last four centers.

He also goes into many patterns, and has developed a notation which I

have not found immediately obvious. I haven't looked at the book more

than to scan it yet, however. He does list a few pretty-patterns, none

of which are checkerboards of any sort.

On a different subject, Paul Schauble accidentally found out how to take

apart the 4^3 today - twist an outer layer about 30 degrees so that an

edge of the twisted face is directly over the edge cube that now forms a

corner on the rest of the cube. Pop out the cube from the outer layer,

twist the face again so that the popped cube's partner is in a similar

position for popping, and then pop it. The corners now come out fairly

easily.

Unlike Plummer's design, the insides of this beastie is a sphere with

grooves running along it to make a kind of universal joint. The center

cubies ride in these grooves and hold all of the other pieces in. We

only took out about a half-dozen cubies because the cube was NOT in an

initialized state, but closer to a pretty pattern. I was definitely

not interested in getting it ALL apart in order to get it back together

correctly. (we did it correctly the first try!). Unlike the 3^3 cube,

the 4^3 does not seem to come apart easily after the first few are out.

I seem to have gone on for a bit longer than I intended. I will study

the pamphlet (published by Dell/Banbury by the way) and report in more

detail on notation later.

I just noticed that in the section on Cubology, the author lists the

number of "arrangements is something in excess of 3.7*10^45". Since

Hoey's number is larger, I guess the statement is correct.

- Ron