🚀 go-pugleaf

Androcles wrote:
> 
> Hana Bizek <hbizek@ameritech.net> wrote in message
> news:38884C17.50BD@ameritech.net...
> > Androcles wrote:
> > >
> > > Sorry Hana, no offense intended.  I just had not heard you mention it,
> > > that's all. :-)
> > > Androcles
> >
> > I am not offended. Amused is more like it.
> >
> > The reason I did not mention the fact is that I felt it to be too
> > obvious. Besides, the original purpose of my post was not to give a
> > lecture, but to ask you if you know of someone, who creates
> > 3-dimensional designs from Rubik's cubes. But I devote a whole chapter
> > in my book to thie fact that elements in a Rubik's cube form a
> > mathematical group. (The book has been published, so it is not a
> > manuscript any more. :-) ) If you can get a hold of it, you will find
> > group information in Chapter 2.
> >
> > Permit me to disclose one tidbit about myself. I studied some group
> > theory as part of my PhD dissertation in theoretical solid-state
> > physics. So I am not a mathematician, but simewhat close. :-)
> > Hana a kostky
> Okay, well, for amusement only:
> There is a well-known little puzzle known as the "Knight's Tour".
> The object of the puzzle is to have the (chess) knight visit all 64 squares
> on the chessboard
> once and once only, according to his usual move, being 1 square in x, two
> squares in y, or 1 square in y and two in x.
> First question:
> After the knight has completed the tour, what is the least number of moves
> needed to return to the starting position?
> Second question:
> Can this result be modified by taking a different tour?
> Suppose we have Rubik's cube, and suggest a tour such that all possible
> outcomes of the various configurations are presented. We begin with the
> identity.
> Question  three, analogous to the knight's tour.
> How many configurations are there, each to be visited once and once only?
> Question four.
> Is this possible?
> Question five:
> How many moves does it take to return to the identity?
> Androcles

I am sorry to respond this late, Androcles, but I needed to think things
over. I am not familiar with the Knight's tour puzzle. Indeed, I have
some hazy notion of how a knight moves, but your explanation of this
point is good and I understand it.
Please look ar these remarks as coming from a relative ignoramus, but if
a tour is a continous parh across a chessboard, then you do not have
that in case of a Pubik's cube. One sequence may position a certain
cubie in ine place, anorther sequence may position it elsewhere on the
whole cube.It's an entirely different approachh, and one that is not
easily equated.
Hana a kostky