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#2
Yoni's Math Forum / Popularity of famous mathematicians by amount of Facebook fans
December 05, 2008, 04:40 AM #3
General Discussion / Re: I miss vL :( Spht Skywing Grok and Yoni come back!!!
August 02, 2008, 07:25 AM
I'm actually here, just less frequently. Though I don't get on Battle.net anymore. Same with Spht and Skywing (haven't heard from Grok for a while though).
Nah @ BNLS. We have more interesting projects now
Haha @ Hostile
Nah @ BNLS. We have more interesting projects now
Haha @ Hostile
@ all
#5
Battle.net Bot Development / Re: If anyone wants to do some data/trend analysis
March 08, 2008, 07:03 AM
Pop it into msexcel and hit the graph button, if you're a man!
#8
Spht's Forum / It's past midnight
December 24, 2007, 05:43 PM
And things aren't Christmasy around here!
#9
Yoni's Math Forum / Re: Graham's number
November 10, 2007, 05:12 PMQuote from: UserLoser on November 08, 2007, 02:29 AMAll your questions are answered in the wikipedia article...
http://en.wikipedia.org/wiki/Graham%27s_number
Seems kinda crazy to me. What "serious" proof was this actually used in and how the hell does someone come up with it? Also what are the arrows going up mean exactly?
#10
Yoni's Math Forum / Re: A nice riddle, invented by a friend of mine
October 31, 2007, 01:26 PM
The solution to the bonus:
Order the ships as in the non-bonus question. Once you hit a boat, try to hit it a second time.
If you succeed twice in a row, that's the exact boat and you can extract its parameters.
If you succeed and then fail, that's not the exact boat and you may keep trying the next boats.
(I'll leave the exact proof of the solution to you.)
Order the ships as in the non-bonus question. Once you hit a boat, try to hit it a second time.
If you succeed twice in a row, that's the exact boat and you can extract its parameters.
If you succeed and then fail, that's not the exact boat and you may keep trying the next boats.
(I'll leave the exact proof of the solution to you.)
#11
Yoni's Math Forum / Re: A nice riddle, invented by a friend of mine
October 15, 2007, 12:58 PM
Very nice and well-worded attempt. Seems to be correct, although I'm not sure you've proven it correctly.
(You can show it easily using linear algebra; if a boat in subset C is hit, the parameters describing the boat satisfy 4 linear equations in 4 parameters, and this system has a single solution which is the parameters of the real boat.)
Anyway, I know a simpler solution (and I hope Ender's solution hints at it).
I'll post it sometime this week unless you can find it.
(You can show it easily using linear algebra; if a boat in subset C is hit, the parameters describing the boat satisfy 4 linear equations in 4 parameters, and this system has a single solution which is the parameters of the real boat.)
Anyway, I know a simpler solution (and I hope Ender's solution hints at it).
I'll post it sometime this week unless you can find it.
#12
Yoni's Math Forum / Re: A nice riddle, invented by a friend of mine
October 12, 2007, 08:33 AM
K is wrong.
Unrelatedly: A single bomb doesn't destroy the ship.
Unrelatedly: A single bomb doesn't destroy the ship.
#13
Yoni's Math Forum / Re: A nice riddle, invented by a friend of mine
October 08, 2007, 01:52 PM
Yeah, you may post it. Go ahead.
As for your attempt of solving the bonus, there is a problem with your solution, but I won't say what it is.
As for your attempt of solving the bonus, there is a problem with your solution, but I won't say what it is.
#14
Yoni's Math Forum / Re: A nice riddle, invented by a friend of mine
October 06, 2007, 03:32 PM
I HAS TEH SOLUTION
[Spoiler alert! Solution below.]
The solution in 1 sentence:
The cardinality of the set of all possible boats is Aleph-0, so order them, and on the n'th second, hit boat n in the position it would be in after n seconds.
Longer explanation:
How many possible boats are there? Each boat is identified by its initial position (a,b) and constant velocity vector (c,d), which are 4 integers. Therefore, the set of boats corresponds to the set of quadruples of integers (Z^4).
The cardinality of Z^4 is Aleph-0, the same as the cardinality of N. This is proven in courses on set theory, and I will not explain the full proof here (there are several proofs, given by giving an example of a one-to-one and onto function between the two sets).
K's partial solution already assumes that Z^2 has cardinality Aleph-0, when he says:
"All that remains is to plug each possible value of (c,d) into the equation"
Convince yourself that Z^2 has cardinality Aleph-0. Then you'll see that Z^4 also has cardinality Aleph-0, since (a,b,c,d) <--> ((a,b), (c,d)) <--> (e,f) <--> g. Get it?
Now that you agree that Z^4 has cardinality Aleph-0, we can order the boats and give all of them index numbers 1,2,3,... (this is because there are countably infinite boats). Each boat has an index number; no boat is missing from the list, and in particular, the actual boat is on the list. It doesn't matter how we order them.
This numbering is enough to start attacking: On the n'th second, try to attack the n'th boat - consider that n seconds have already passed, so attack the position it would be in after n seconds (as K has explained). Eventually, n will equal the actual boat's index, and the attack will succeed.
For bonus points: Improve the algorithm so that it also finds the starting point and velocity
[Spoiler alert! Solution below.]
The solution in 1 sentence:
The cardinality of the set of all possible boats is Aleph-0, so order them, and on the n'th second, hit boat n in the position it would be in after n seconds.
Longer explanation:
How many possible boats are there? Each boat is identified by its initial position (a,b) and constant velocity vector (c,d), which are 4 integers. Therefore, the set of boats corresponds to the set of quadruples of integers (Z^4).
The cardinality of Z^4 is Aleph-0, the same as the cardinality of N. This is proven in courses on set theory, and I will not explain the full proof here (there are several proofs, given by giving an example of a one-to-one and onto function between the two sets).
K's partial solution already assumes that Z^2 has cardinality Aleph-0, when he says:
"All that remains is to plug each possible value of (c,d) into the equation"
Convince yourself that Z^2 has cardinality Aleph-0. Then you'll see that Z^4 also has cardinality Aleph-0, since (a,b,c,d) <--> ((a,b), (c,d)) <--> (e,f) <--> g. Get it?
Now that you agree that Z^4 has cardinality Aleph-0, we can order the boats and give all of them index numbers 1,2,3,... (this is because there are countably infinite boats). Each boat has an index number; no boat is missing from the list, and in particular, the actual boat is on the list. It doesn't matter how we order them.
This numbering is enough to start attacking: On the n'th second, try to attack the n'th boat - consider that n seconds have already passed, so attack the position it would be in after n seconds (as K has explained). Eventually, n will equal the actual boat's index, and the attack will succeed.
For bonus points: Improve the algorithm so that it also finds the starting point and velocity
#15
Yoni's Math Forum / Re: A nice riddle, invented by a friend of mine
October 06, 2007, 10:23 AMQuote from: K on October 04, 2007, 08:47 PM
We'll also assume that there is an upper bound on the magnitude of the velocity, which I hope is not cheating. If the boat is traveling at an infinite rate we're in trouble.
Many people I have told the riddle to have a difficulty with the distinction between "infinite" and "finite, but unbounded".
There is no upper bound on the velocity. But, it is finite.
That is, the velocity being (c,d), c and d are finite integers. But there is no upper bound on either one of them.
Get it?
I'll post the full solution later this evening.