Re: compactness in angels/devil problem
- From: pauldepstein@xxxxxxx
- Date: Sat, 2 Feb 2008 21:37:54 -0800 (PST)
On Feb 2, 3:26 pm, William Elliot <ma...@xxxxxxxxxxxxxxxxxx> wrote:
On Fri, 1 Feb 2008 pauldepst...@xxxxxxx wrote:
On Feb 1, 10:06 pm, David C. Ullrich <dullr...@xxxxxxxxxxx> wrote:
What's the angels-and-devils problem?
Informal version of angels/deviltheory: The angel is on a square
chessboard which is infinite in all directions (Z x Z in other words).
For each square of the chessboard, there is a finite set of squares
which the angel can visit on the next move (you get a different problem
or question for each rule determining the finite set). Thedeviland
the angel take alternate moves. Thedevilmoves by eating one
non-occupied square and therefore preventing the angel landing on it.
Can thedevilrun the angel out of moves? (As stands, not a meaningful
problem because I haven't given a rule determining the angel's possible
moves.)
Concrete example: Suppose the angel moves like a king in the version of
chess played in the US, England, Eastern Europe and elsewhere (in fact,
the most globally widespread version of chess.) Then thedevilcan trap
the angel.
I don't believe it.
----- Hide quoted text -
- Show quoted text -
There's a proof in Winning Ways, I think. I'm sure you either have it
or have access to it. (I myself don't -- I'm not at a university and
don't have access to many texts.)
Paul Epstein
.
- References:
- compactness in angels/devil problem
- From: pauldepstein
- Re: compactness in angels/devil problem
- From: David C . Ullrich
- Re: compactness in angels/devil problem
- From: pauldepstein
- Re: compactness in angels/devil problem
- From: William Elliot
- compactness in angels/devil problem
- Prev by Date: cost accounting solutions manual
- Next by Date: Re: Problems with calculating the proper compounding
- Previous by thread: Re: compactness in angels/devil problem
- Next by thread: Re: compactness in angels/devil problem
- Index(es):
Relevant Pages
|
Loading
