Date: Fri, 20 Oct 95 18:29:45 +0200
From: Mikko Haapanen <hazard@niksula.hut.fi >

>I want to ask if somebody can tell me how to flip 2 adj. edges (and nothing
After buying my first cube, it took me about a week to figure out how
The 4x4x4 was a little tougher. It took me about a week to figure out
how to solve everything except two edge cubies which were exchanged.
It took me about another year(!) to figure out how to exchange them.

It took me about 6 years. That problem was a little background process in my
brains. Then i went to the army. In the evenings i used to 'play' with 4x4x4
until one day. I noticed the same thing as you. 2 flipped edges can be
solved by turning one inner slice 90 degrees. Since then i haven't
anyone could do it less than 39 turns.

What I didn't see originally was that there could be invisible
movement of the face centers to compensate for the "bad parity" of
the edges. I am very poor at solving the 4x4x4, but here is how I

I have thought the center piece movements too. It must be very hard to see a
parity from certers, even if they were marked (position and orientation).
There are so many different 'right' positions too.

This reminds me another old question: 3x3x3 are told to have about 4
trillion (or whatever) different positions. How many of these positions are
'solved cube' but with different centerpiece combinations? Once i had 3x3x3
with 6 different pictures (picture/side). Friends asked me to solve it. When
i was completed, they laughed at me and pointed the bottom center piece,
which was out of orientation (i can't remember how many of centers were out
of order).

Finally, here is my question. On the 4x4x4, I get "bad parity" darn
near every time. Why isn't it 50-50 like the situation I have with

```I don't know, but i guess: 1/4 you get it right and 3/4 goes wrong. I think
we must count that there are 2 inner slice states: right and wrong. There
are also 2 outer slice states: right and wrong (2 corners at wrong
position). It makes me think that 1/4.
------Mikko Haapanen------hazard@niksula.hut.fi---------
Jos tahto siirtää vuoren, niin tahdon siirtää tahdon
Vuorta siirtämään, että vuoren sisään nään -P.Hanhiniemi
--------------------------------------------------------
```