Are you smart enough? III and last (693 hits)
Category: NoneRating: -0.29 on 23 reviews (Rate this item) (V)
Submitted by STANDARD D II (View user info) at 2006-01-20 05:30:08 EST
This will be the last of three problems because unless you get into outright religion this is as hard as you can get.
The other two found here
http://www.ubersite.com/m/82448
And here
http://www.ubersite.com/m/82087
were hard, but do not compare to this. Here is the gauntlet. Good luck
I have found one that no one has yet to solve. If you get this one you can go to the website posted at the bottom and redeem a thousand dollars.
Applied Mathematics Game Theory
MathWorld Contributors Barile
Angel Problem
In a game proposed by J. H. Conway, a devil chases an angel on an infinite chessboard. At each move, the devil can eliminate one of the squares, and the angel can make a leap in any direction, covering a distance of at most squares. Here, is a positive integer previously fixed, and is called the "power" of the angel. The devil's aim is to trap the angel on an island surrounded by a hole of width at least .
Can the angel indefinitely escape the devil, if his power is sufficiently high? Can the devil defeat an angel of any finite power? These questions are still unanswered. In particular, it is unknown if this is a fair or unfair game.
http://mathworld.wolfram.com/AngelProblem.html
User Reviews
Submitted by Shlongy (user info) at 2006-01-20 12:34:34 EST (#)
Ranking: -2
Auto -2 for no reason whatsoever.
Submitted by simple_catalyst (user info) at 2006-01-20 12:34:22 EST (#)
Ranking: 2
Submitted by HighVoltage900 (user info) at 2006-01-20 11:30:44 (#)
Ranking: 0
Well you are missing the basical principles of angels and devils which help answer the question.
Devils-Evil. And we all know evil guys don't follow the rules. So while he is only SUPPOSED to move one space at a time, he is probably speeding and going two, maybe even three spaces at a time. Cause he is a bad ass like that. And he has a Spas-12. When he gets within 12 spaces of the angel, I am 95% he will blow the winged mother fucker out like a Columbine school boy.
Angels-Pussy ass good guys. Doesn't like to take risks and is generally a push over. I'm sure if the devil asked nicely for the angel to come over the angel would oblige him. Then the devil would sodomize the angel and god would punish two human cities for it. I'm thinking L.A. and London. They need to go. Also the angel has ADD and would get distracted from the devil at some point, thereby allowing the devil to catch up to him and insert penis.
So obviously as I have shown, eventually the devil WILL catch/kill/sodomize the angel. He doesn't even need a perimeter to do it.
God I am the only one who gets this?
Submitted by nitty34 (user info) at 2006-01-20 12:26:19 EST (#)
Ranking: 0
I agree it has to be larger than 'n'
Thus my theory of not stopping until the span of the moat is 4(n*n)+? - 4(n*n) > n
And if the angel started at origin point 0 jumping by a distance of n, it would not even reach the moat until the moat was too large to jump - if the starting point of the moat was 4(n*n)+1.
Again, I think.
What if C-A-T really spelled 'dog?'
Tough one, Ogre.
Submitted by Spam (user info) at 2006-01-20 12:06:44 EST (#)
Ranking: -2
that wasn't supposed to be a +2
Submitted by Spam (user info) at 2006-01-20 12:06:19 EST (#)
Ranking: 2
Submitted by nitty34 (user info) at 2006-01-20 11:58:35 (#)
Ranking: 0
Spam -
I multiplied it by 4 because the goal is for the devil to build a square moat with a span of at least 'n' around the angel. There are 4 sides to a square. Perhaps it's oversimplified, perhaps it's unnecessary, but multiplying it by 4 would allow sufficient time for the squares to be removed on all 4 sides of the angel.
I think.
--
You could use a circle of course, which would be more efficient and again, I think that your theory may work if all you had to do was build a moat but you seem to be forgetting that this moat must also be UNJUMPABLE by the angel. Therefore it has to have a depth of at least n+1 otherwise the angel would just jump over it (another detial that appears to have been missed is that the angel can pass over squares that have been destroyed unimpeded so long as he finishes on a square that exists.
Submitted by nitty34 (user info) at 2006-01-20 11:58:35 EST (#)
Ranking: 0
Spam -
I multiplied it by 4 because the goal is for the devil to build a square moat with a span of at least 'n' around the angel. There are 4 sides to a square. Perhaps it's oversimplified, perhaps it's unnecessary, but multiplying it by 4 would allow sufficient time for the squares to be removed on all 4 sides of the angel.
I think.
Submitted by HighVoltage900 (user info) at 2006-01-20 11:30:44 EST (#)
Ranking: 0
Well you are missing the basical principles of angels and devils which help answer the question.
Devils-Evil. And we all know evil guys don't follow the rules. So while he is only SUPPOSED to move one space at a time, he is probably speeding and going two, maybe even three spaces at a time. Cause he is a bad ass like that. And he has a Spas-12. When he gets within 12 spaces of the angel, I am 95% he will blow the winged mother fucker out like a Columbine school boy.
Angels-Pussy ass good guys. Doesn't like to take risks and is generally a push over. I'm sure if the devil asked nicely for the angel to come over the angel would oblige him. Then the devil would sodomize the angel and god would punish two human cities for it. I'm thinking L.A. and London. They need to go. Also the angel has ADD and would get distracted from the devil at some point, thereby allowing the devil to catch up to him and insert penis.
So obviously as I have shown, eventually the devil WILL catch/kill/sodomize the angel. He doesn't even need a perimeter to do it.
God I am the only one who gets this?
Submitted by Caulaincourt (user info) at 2006-01-20 11:19:47 EST (#)
Ranking: 0
Think of it as a huge room where the devil is slowly painting the floor around the perimeter until the angel is stuck in the middle."""
Oh really? That's just kind of like rephrasing the question there.
The question is to know whether the angel would have time to escape indefinitly or not.
The angel walks the ray at n of any circle that devil tries to build around him. hose "perimeters" take expotentially more turns to widen (wow, my english math vocabularry is caca)
It's a math problem, not a 4th grade riddle. You just got the question.
And I don't have the answer.
Submitted by Spam (user info) at 2006-01-20 10:56:50 EST (#)
Ranking: -1
Submitted by nitty34 (user info) at 2006-01-20 10:06:20 (#)
Ranking: 1
And to answer:
It seems like the real question is not whether the devil can trap the angel on an island surrounded by a 'moat' of removed squares greater than 'n' but whether this is a fair or unfair game.
I think it's an unfair game, as not enough information is given to formualte an educated decision.
You'd need to know:
1. Can the devil remove any square, from any place on the infinite board?
2. Does the devil know the value of the angel's power 'n' ?
If the answer to both is yes, then the devil can, eventually, trap the angel on the board.
From angels starting point, the devil would remove 1 square at a distance of 4(n*n). The next turn, remove the square at 4(n*n)+1. Then 4(n*n)+2. And so forth until 4(n*n)+? - 4(n*n) > n
BUT: If the angel moved forward the first time and then moved to the right (always at a distance of n) the second time - the devil would need to remove a square in that direction - at the same distance 4(n*n). Another jump right - 4(n*n)+1 in that direction.
Think of it as a huge room where the devil is slowly painting the floor around the perimeter until the angel is stuck in the middle.
But again, this is based on the 2 stipulations I've listed. Otherwise, it's an unfair game.
--
It's not dependant on those stipulations at all but according to the problem YES the devil may remove any square he wishes. It also strikes me that the Devil will know the value n as even if he doesn't know it from the outset it will become apparant after the fist few of the angel's 'moves'. Even if takes a million moves for the Devil to work out exactly the value of n, his position is no weaker than at the start seeing as the board is infinatly large and there is no time frame set in which the Devil must achieve victory.
That said, your theory seems overly simple to me and I am intrigued as to why you would multiply the paranthises by 4. Why 4? why not 400? Also. Have you considered that the width of the gap must be greater than n all the way around the island?
Rating because all you had to do was cut and paste the text from the link you gave (which includes the missing terms) and YOU STILL FUCKED IT UP.
Submitted by DCWoody (user info) at 2006-01-20 10:55:35 EST (#)
Ranking: 0
ahhhh, I new I was missing somehting, for some reason I though the angel could jump over at least one square at a time.
Submitted by nitty34 (user info) at 2006-01-20 10:06:20 EST (#)
Ranking: 1
And to answer:
It seems like the real question is not whether the devil can trap the angel on an island surrounded by a 'moat' of removed squares greater than 'n' but whether this is a fair or unfair game.
I think it's an unfair game, as not enough information is given to formualte an educated decision.
You'd need to know:
1. Can the devil remove any square, from any place on the infinite board?
2. Does the devil know the value of the angel's power 'n' ?
If the answer to both is yes, then the devil can, eventually, trap the angel on the board.
From angels starting point, the devil would remove 1 square at a distance of 4(n*n). The next turn, remove the square at 4(n*n)+1. Then 4(n*n)+2. And so forth until 4(n*n)+? - 4(n*n) > n
BUT: If the angel moved forward the first time and then moved to the right (always at a distance of n) the second time - the devil would need to remove a square in that direction - at the same distance 4(n*n). Another jump right - 4(n*n)+1 in that direction.
Think of it as a huge room where the devil is slowly painting the floor around the perimeter until the angel is stuck in the middle.
But again, this is based on the 2 stipulations I've listed. Otherwise, it's an unfair game.
Submitted by nitty34 (user info) at 2006-01-20 09:53:34 EST (#)
Ranking: 0
When you cut and paste a problem, make sure variables transfer within the cut and paste.
Here is how it SHOULD read:
In a game proposed by J. H. Conway, a devil chases an angel on an infinite chessboard. At each move, the devil can eliminate one of the squares, and the angel can make a leap in any direction, covering a distance of at most 'n' squares. Here, 'n' is a positive integer previously fixed, and is called the "power" of the angel. The devil's aim is to trap the angel on an island surrounded by a hole of width at least 'n'.
Can the angel indefinitely escape the devil, if his power is sufficiently high? Can the devil defeat an angel of any finite power? These questions are still unanswered. In particular, it is unknown if this is a 'fair' or 'unfair' game.
Submitted by DCWoody (user info) at 2006-01-20 09:20:29 EST (#)
Ranking: 0
RAD is right, but this still seems stupidly easy to me, but as theres a £550 prize I'll assume I'm missing soething
Submitted by indoninja (user info) at 2006-01-20 08:49:50 EST (#)
Ranking: -2
Either Rad was right or you left something out in the explanation.
Submitted by rad1101 (user info) at 2006-01-20 08:47:34 EST (#)
Ranking: -2
people, this isn't really that difficult to understand what the problem is asking.
you make your own variables, as long as they are positive integers. THen you prove or disprove the supposition.
not a difficult concept, just a mathematical proof.
-2 for
1. boring math problems
2. not understanding yourself what it is asking, let alone trying to solve the thing
Submitted by Siren (user info) at 2006-01-20 08:47:09 EST (#)
Ranking: 0
I don't know what "a distance of at most squares" is.
I know! It's an impossible to solve this because of it's sentence structure!
Submitted by DCWoody (user info) at 2006-01-20 08:21:32 EST (#)
Ranking: 0
Unless the angel is really stupid it could out outrun it forever.
Im I missing something here or is this stupidly easy?
A positive integer must be at least one.....wait a minute, if its infinite then the devil could start making a really huge box...it depends on the actions of the angel I think, as long as it jumped in roughly a straight line, and was smart enough /could see the whole board to avoid any traps then I think the devils screwed.
Or am I missing something?
Submitted by skrapmetal (user info) at 2006-01-20 07:41:50 EST (#)
Ranking: 2
You said "hole".
Submitted by CLAIRE1 (user info) at 2006-01-20 06:56:55 EST (#)
Ranking: 0
I thought it had some things missing too. But I am not smart enough to even come close to figuring it out so just kind of blew it off.
Submitted by redskieslookfake (user info) at 2006-01-20 06:53:02 EST (#)
Ranking: -2
-2 for not giving us any variables whatsoever. Unless that's actually the question. Guess what you're thinking.
Submitted by Jacobt26 (user info) at 2006-01-20 06:30:29 EST (#)
Ranking: 0
This problem is retarded. An infinite chessboard, the ability to jump most of the squares, and the ability to remove 1 square. The board is infinite, the angel can move an infinite distance, there would never be a lack of places for it to go.
Submitted by phuzzygish (user info) at 2006-01-20 06:03:59 EST (#)
Ranking: 0
"a hole of width at least" ?
Submitted by phuzzygish (user info) at 2006-01-20 06:03:32 EST (#)
Ranking: 0
Dude, this is written very badly, and I think it leaves out some figures?