Originally posted by broblutoBoard is infinite so first angel move is irrelevant.
If angel moves to (1,1), burn (40,40). angel moves to (2,2), burn (40,39), angel moves to (3,3), burn (39,40) etc
1d (-40,-40)
1a (1,1)
2d (40,40)
2a (2,0)
Then what?
3d (40,0)
3a (3,-1)
4d(40,-1)
4a(2,2)
...
If it moves in a spiral, I don't see how you can catch the angel. Feel free to change any play or continue from 5d.
Originally posted by wolfgang59What are suares?
And what if the Angel can move 3 suares on every prime number move?
😕
Or are you so imprecise, that you can't even be bothered to proof-read your 14 word post?
Maybe you could reverse this perception of yourself by answering at least one of my questions. I tried it last night and I don't think the devil can stop the angel even in the basic situation, but I must admit I didn't spend a long time on it.
Originally posted by PalynkaI don't understand what you mean by spiral. If you build a fence around the angel with corners at (40,-40), (-40,40), (40,40), and (-40,-40) the angel won't be able to escape.
Board is infinite so first angel move is irrelevant.
1d (-40,-40)
1a (1,1)
2d (40,40)
2a (2,0)
Then what?
3d (40,0)
3a (3,-1)
4d(40,-1)
4a(2,2)
...
If it moves in a spiral, I don't see how you can catch the angel. Feel free to change any play or continue from 5d.
Originally posted by GastelI feel sad for anyone that proof-reads their posts on here .. its meant to be converstaional fun isn't it?
What are suares?
Or are you so imprecise, that you can't even be bothered to proof-read your 14 word post?
Maybe you could reverse this perception of yourself by answering at least one of my questions. I tried it last night and I don't think the devil can stop the angel even in the basic situation, but I must admit I didn't spend a long time on it.
However before you call the pot black check your own grammar.
And of course the devil can stop the Angel. I'll accept a challenge from anyone and fry your ass within 30 moves!
Originally posted by broblutoMy contention is that I don't see how you can do that if the angel can move diagonally. If you think so, then play the next move.
I don't understand what you mean by spiral. If you build a fence around the angel with corners at (40,-40), (-40,40), (40,40), and (-40,-40) the angel won't be able to escape.
2 edits
Originally posted by PalynkaWell,
My contention is that I don't see how you can do that if the angel can move diagonally. If you think so, then play the next move.
3d would be (40,-40)
3a (2,-1)
4d (-40,40)
4a (3,-2)
demon would continue to burn squares along the lines, x=40, x=-40, y=40, and y=-40...
I'll add something in here, because I think I know what you're saying.
...skipping every other square and alternating.
The best chance for the angel to escape is to move diagonally in one direction as best as possible.
1d (-40,-40)
1a (1,1)
2d (40,40)
2a (2,2)
3d (40, 38)
4a (3,3)
4d (38,40)
5a (4,4)
5d (40, 36)
etc.
as the angel approaches a side, start to close them up by burning the squares in between the already burnt ones.
Even if the angel gets to (20,20) and decides to change direction, seeing its impending doom, and moves in the direction of (21,19) towards (40,0), the demon would start burning at (40,0) and alternate burning every other square towards (40,40) until the angel gets close and the demon should fill them in.
I did it in Excel.
The demon's moves are dependent upon the angel, but it should always be on the lines mentioned above.
Edit: Obviously until it is closed up and then start burning inside the fence to eventually force the angel to commit suicide.
Originally posted by GastelFor the basic problem, wherein the angel moves one space orthogonally for every demon burning, the demon can very easily trap and therefore take out the angel.
I tried it last night and I don't think the devil can stop the angel even in the basic situation, but I must admit I didn't spend a long time on it.
First burn, he can burn a square diagonally adjacent.
Should the angel move alongside, he blocks directly ahead. When the angel moves again, he burns a square diagonally to the outside and repeats the process. After 8 burns, the angel will find himself unable to move fast enough to make it through the holes and is trapped. Moving towards the imagined "center" of this circle of burned squares only expedites the process.
Should the angel's first move be away from the first burned square, the demon can burn diagonally ahead, in line with the first, creating what amounts to a virtual wall, because the demon can cut the angel off from passing before the angel can make it through. If the angel continues in a straight line, burning directly ahead cuts off his escape, and either puts him in a similar trap to the above paragraph, or else returns him to his previous square, only the demon has him more caged in that before.
It takes forethought and perhaps a bit of patience, but the basic problem is an easy win for the demon.
I don't know about the versions where the angel is faster, however.
2 edits
Quite right geep. However, your method of explaining... well, i think it is difficult to be very rigourous and clear. I have the following proof, (was probably mentioned before)
We can assume that the demon starts, as the board is infinite and any first move by the angel changes nothing. Now on his first 4 moves, the demon burns the following squares (assuming the angel is at (0,0))
(-4,5)
(5,4)
(4,-5)
(-5,4)
At this stage the angel has made three moves, and he is therefore in or on the boundary of a square(diamond) with corners of coordinates (0,3),(3,0),(0,-3),(-3,0)
Now the demon can do the following:
Whenever the angel stands on a square that has x-coordinate 4, the demon burns the square next to the angel with x-coordinate 5. Similarly for the other four sides. It is now impossible for the angel to escape out of the box created by the demons first 4 burnings.
I assume someone can tweak this for the diagonal case.
Originally posted by wolfgang59Wolfgang, here is my challenge. Angel can move diagonally, and repairs a square every other move. The devil burns a square every turn, but it cannot be more that 5 squares from the square he burned the night before.
I feel sad for anyone that proof-reads their posts on here .. its meant to be converstaional fun isn't it?
However before you call the pot black check your own grammar.
And of course the devil can stop the Angel. I'll accept a challenge from anyone and fry your ass within 30 moves!
I'll be the angel, and I want wolfy to fry me... although, I think he won't be able. Now wolfmeister has opened the challenge, and I have accepted. Will he respond or not?
Originally posted by GastelI dont accept the challenge because its totally different to the original problem!!!
Wolfgang, here is my challenge. Angel can move diagonally, and repairs a square every other move. The devil burns a square every turn, but it cannot be more that 5 squares from the square he burned the night before.
I'll be the angel, and I want wolfy to fry me... although, I think he won't be able. Now wolfmeister has opened the challenge, and I have accepted. Will he respond or not?
Originally posted by wolfgang59Of course not. I knew you wouldn't (notice the apostrophe). When you boldly stated that you challenge anybody, you did not state the terms.
I dont accept the challenge because its totally different to the original problem!!!
So chickenlittle59, I guess your mettle has been proven.
Gastel, Wolfgang's challenge was in response to your comment that even the basic problem was impossible for the demon. As such his challenge carries with it identical conditions, and the excuse that "he didn't state the conditions" is rather lame and tangential to the point he seems to be making in the challenge.
He was saying the basic problem is very much in favor of the demon, and a challenge where the angel has significantly more mobility and a repair ability is irrelevant to the basic problem.