🚀 go-pugleaf

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