|
![]() |
#1 | ||
![]() ![]() ![]() ![]() ![]() ![]() Join Date: Sep 2004
Location: Valleyfield, Canada
Posts: 4,892
|
![]() Angel cannot win unless you can define infinity.
Angel lose. End of story. |
||
![]() ![]() |
|
![]() |
#2 | ||
![]() ![]() ![]() ![]() ![]() ![]() Join Date: May 2008
Location: Waterside, South Africa
Posts: 3,138
|
![]() Mmm, chessboard of infinite size? If length of side is n, then n is infinity, yes? But, the number of squares on the board is also infinite, as is the surface area of the board, n x n. What you're essentially saying is there would only be one square left, for the piece A to stand on: Therefore d must be able to remove n-1 squares from the board, in order to win. This is a paradox, because if that's possible, infinity - n - must be quantifiable. Because otherwise there will always be more squares for A to move to. Infinity minus one is still infinity. If you can count them, however, it's not infinity. The board is huge, of course, but not infinite. It can be argued that the universe itself is not infinite, so now we're talking quantum? In which case, I'd rather talk about something else.
|
||
![]() ![]() |
|
![]() |
#3 | ||
Join Date: Oct 2004
Location: Opole, Poland
Posts: 14,276
|
![]() If the devil focuses on building a large "moat" of pits and then takes out the borders of the large "island" formed that way before the angel can run out... yeah, he can win.
|
||
![]() ![]() |
|
![]() |
#4 | ||
![]() ![]() ![]() ![]() ![]() ![]() Join Date: May 2008
Location: Waterside, South Africa
Posts: 3,138
|
![]() Was I wrong in understanding that angel can jump over any number of empty spaces?
|
||
![]() ![]() |
|
![]() |
#5 | ||
Join Date: Oct 2004
Location: Opole, Poland
Posts: 14,276
|
![]() The angel's [N] can be anything from 1 to infinity. For angels with low [N], it's definitely possible to trap them.
|
||
![]() ![]() |
|
![]() |
#6 | ||
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() Join Date: Nov 2007
Location: Phoenix, United States
Posts: 238
|
![]() Who is the first player? who would like to play against Devil?
If it is God then the possibilites are infinite :amused:. But if there is no first player then Angel cannot move whatever is the N NUMBER.
__________________
Abandonia is the best!!!:thumbs: "There work was play And play the only work" Sri Aurobindo |
||
![]() ![]() |
|
![]() |
#7 | ||
![]() ![]() ![]() Join Date: Jan 2008
Location: Christchurch, New Zealand
Posts: 1,044
|
![]() The angel will be able to keep moving in any given vector as long as it can move more than one square per turn. Because the devil can only remove one, the angel can simply jump over it if it's [N] is higher than the row of holes, otherwise it can simply move off in another direction. And even if the angel only has an [N] power of 1, it would take a long time and some exceedingly good forward thinking by the devil to trap it.
|
||
![]() ![]() |
|
![]() |
#8 | ||
![]() ![]() ![]() ![]() ![]() ![]() ![]() Join Date: Mar 2006
Location: ,
Posts: 4,615
|
![]() A fine point is that, if the angel needs to keep on going infinitely to win, he won't ever win.
Quote:
Quote:
I'm not going to think of all the possible strategies now, so I don't have an answer, but I wouldn't bet for the devil--perhaps out of principle. :bleh:
__________________
Life starts every day anew. Prospects not so good... |
||
![]() ![]() |
|
![]() |
#9 | ||
![]() ![]() ![]() ![]() Join Date: Aug 2007
Location: Dixmuide, Belgium
Posts: 2,767
|
![]() The angel can't win.
Period. The devil will get the angel and the devil will screw the angel. Devils cheat, ya know, that's why they are devils. :nuts:
__________________
Not a member of The Victorious People's Shoutbox Liberation Army. Not a member of the GAG Guerrilla. Don't get A Grip! FOR RENT *Advertising space* |
||
![]() ![]() |
|
![]() |
#10 | ||
![]() ![]() ![]() ![]() ![]() ![]() Join Date: Dec 2007
Location: Cut and Shoot, United States
Posts: 32
|
![]() Quote:
This can be seen by counting: To capture the angel the devil has to surround it some closed shape. We assume for simplicity it is a squared rectangle. Of course a circle would be better, but it is more hard to calculate with, and a square is less than a factor of two worse. Now when the devil builds a squared rectangle of length l, it needs N*4*(l-1) moves (and a few more if N>1, too lazy to derive the exact formula). The minimum length is obviously 3, the angel has to fit inside. Unfortunately (for the devil) this gives the angel more than enough time to leave the rectangle. And as we can safely assume that he will need more than N*2*(l-1) moves for any kind of closed shape of maximum diameter l, the angel can escape any shape the devil might come up with, simply because it will be unfinished when the angel reaches the border. Without enclosing shape the angel can move infinitively, of course, as the chessboard is infinite. This assumes the angel knows the moves of the devil and plays perfectly (as fitting for an angel), but then the devil cannot win. Closing the shape simply takes too long. If a part of the shape is closed the angel will head in the other direction. And even building a shape partially (setting every second stone e.g.) and the filling when the angel approaches is not fast enough, if the angel races consequently towards infinity (as it must when playing perfectly) the devil cannot build fast enough. Last edited by arete; 01-12-2008 at 07:52 AM. Reason: ambiguity |
||
![]() ![]() |
|
![]() |
![]() |
||||
Thread | Thread Starter | Forum | Replies | Last Post |
PIGSgrame | PIGSgrame | Offers | 7 | 21-01-2011 09:38 AM |
Ripley's Believe It or Not! - The Riddle of Master Lu | TotalAnarchy | R | 4 | 12-11-2010 02:23 PM |
Ripleys Believe It or Not - The Riddle of Master Lu | Spaceball | Approved Requests | 8 | 23-09-2007 11:00 PM |
Riddle | a1s | Forum Games | 839 | 14-08-2007 12:10 PM |
Never ending riddle? | Unknown Hero | Blah, blah, blah... | 377 | 19-10-2004 11:04 AM |
|
|
||
  |