This is a self-correction from NL Subscriber "Larry Robinson" who sent me a MooseTik on a Rubik's Cube useless fact I posted a few weeks back! Larry has to be a walking computer!

quote:

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I goofed in the analysis of the Rubik's Cube. Here is the correction:

"A. There may be 1,929,770,126,028,800 'color combinations'
(whatever that is - please explain) on a Rubik's cube, but:"

I found out that this was the number that Ideal Toys published in the book
that came with the cube. Where they got it I have no idea.

"An original Rubik's cube (with one solid color on each face when
solved) can be put in 21,626,001,637,244,928,000 distinct
positions (not counting rotations of the center axle structure,
which provides duplicate positions only rotated in space)."

It turns out I omitted one factor of 2. Here is the correct analysis, in
full:

8 corner cubies can be in P(8,8) locations: 40,320
8 corner cubies can be rotated in 3^7 ways*: 2,187
12 edge cubies can be in P(12,10) locations** 239500,800
12 edge cubies can be rotated in 2^11 ways*: 2,048
6 center cubies don't move, rotations are invisible.*** 1
The product: 43,252,003,274,489,856,000

* The last cubie's rotation in place is forced.
** For any given position of the corner cubies, the last pair is forced.
*** Moving the center cubies is equivalent to rotating the whole cube.

That's approximately 43.3 quintillion in the US or France (43.3 trillion
in the rest of the world), or 43.3 times 10 to the 18th power. In
the lore of large numbers, this is sometimes called the Rubik
Constant.

As a result, this was wrong too:

"A Rubik's cube with a different photograph on each face can be
put in 44,290,051,353,077,612,544,000 distinct positions (not
counting rotations of the center axle structure, which provides
duplicate positions only rotated in space)."

The same factor was missing here:

The Rubik Constant: 43,252,003,274,489,856,000
6 center cubies can be rotated in 4^5 * 2 ways****: 2,048
The product: 88,580,102,706,155,225,088,000

**** The last cubie is restricted to half turns.

That's approximately 88.6 sextillion in the US or France (88.6 trilliard in
the rest of the world), or 88.6 times 10 to the 21st power.

It is possible to take a Rubic's Cube, or a picture cube apart, and
reassemble it so it can't be solved. All that has to happen is that at least
one of the three (four on a picture cube) "forced" cubies is put in the
wrong location or orientation.

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[This message has been edited by TexasJoe (edited 05-02-2000).]

Yeah right TJ. I agree with whatever you say.. You lost me way back.. LOL

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Pinhead,Pindead,PinM&M, PinMoney, Pinocchio Pincushion, Pinwheel, Pinochle

Hey,Tex, think the Cube was the only puzzle cube? You probably don't remember the Soma cube(not named, no doubt, for the drug in Huxley's Brave New World!), created by Danish poet-scientist Piet Hein. It consisted of differently shaped sections that could be put back together in many shapes, like a Chinese tangram. Hein also authored the Grooks series, little wittily aphoristic poems on some philosophical point. tjoeb};>