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by benczur
January 15th, 2008, 12:51 pm
Forum: Brainteaser Forum
Topic: n-gon question
Replies: 3
Views: 62664

n-gon question

<t>For the area, calculate the distance from the center to the sides of the small and large n-gon, take the ratio and square.Distance to the sides of large n-gon: R*cos(pi/n).Distance to the sides of small n-gon: R*sin(pi/n), if n even,R*sin(pi/2n), if n odd.Area of small n-gon as a fraction of larg...
by benczur
December 23rd, 2007, 7:45 pm
Forum: Careers Forum
Topic: Object Oriented Programming in C++
Replies: 22
Views: 64256

Object Oriented Programming in C++

<t>Thank you all for the book recommendations and their critiques. Also thanks for the s/w recommendartions, twofish.As I see this thread spun another thread about how much a quant should really know about C++, I might add that the interviews mentioned in the OP were not for (real) quant jobs. Never...
by benczur
December 21st, 2007, 1:06 pm
Forum: Brainteaser Forum
Topic: Random Intervals
Replies: 44
Views: 69546

Random Intervals

<t>QuoteOriginally posted by: NE1I am confused by the question. Are you asking for the probability that there is exactly one interval that overlaps all the others or are you asking for the probability of AT LEAST one? So which is it? Exactly one or at least one as in one or more?Well, the result of ...
by benczur
December 20th, 2007, 7:24 pm
Forum: Brainteaser Forum
Topic: Random Intervals
Replies: 44
Views: 69546

Random Intervals

<t>QuoteOriginally posted by: ChicagoGuyMy conjecture is that, given some random intervals (being either a good or bad combo), then if you inject a random interval [x, 2n+1], hence forcing [y, 2n+2] then the resulting random intervals are going to be good with p=2/3 just as above. I understood your ...
by benczur
December 20th, 2007, 5:06 pm
Forum: Brainteaser Forum
Topic: Random Intervals
Replies: 44
Views: 69546

Random Intervals

<r>MCarreira,I see we understand much better each other in Mathematica So here is my code for generating the intervals, good and bad, as well iterating from n to n+2. On my (very slow) laptop I can check up to 10->12 in less than 1 minute. Let me know if it works with you!Edit: oops, my i indices wh...
by benczur
December 20th, 2007, 2:17 am
Forum: Brainteaser Forum
Topic: Random Intervals
Replies: 44
Views: 69546

Random Intervals

Yep, I am taking a pattern and its symmetric to be different ones. I think we need this to obtain 2/3.
by benczur
December 19th, 2007, 10:53 pm
Forum: Brainteaser Forum
Topic: Random Intervals
Replies: 44
Views: 69546

Random Intervals

<t>QuoteOriginally posted by: MCarreiran=2: {1,2} => 1 pattern, 1 goodI would exclude n=2 as an exception. Obviously here is the probability is 1.Quoten=4: A={{1,2},{3,4}} => bad (add {n+1,n+2}) B={{1,3},{2,4}} => good C={{1,4},{2,3}} => good (add {0,n+1}) 3 patterns, 2 goodagreedQuoten=6: {{1,2},{3...
by benczur
December 19th, 2007, 3:52 pm
Forum: Careers Forum
Topic: PhD programs
Replies: 6
Views: 62664

PhD programs

<t>QuoteI don't think that there are "best Schools". You have to understand that a Phd program is basically you, your computer and, maybe, if you're lucky, your supervisor.Part of the deal is you figuring out things on your own.[...]I think you should be looking at potential supervisors, not school ...
by benczur
December 18th, 2007, 8:22 pm
Forum: Careers Forum
Topic: Object Oriented Programming in C++
Replies: 22
Views: 64256

Object Oriented Programming in C++

<t>I have a "good friend" of mine, who has a problem with object oriented programming in C++, as opposed to object based programming.More exactly he used C and C++ for quite a few years for different pet projects, numerical simulations in his research etc. He wrote pieces of code that received accol...
by benczur
December 18th, 2007, 5:53 pm
Forum: Programming and Software Forum
Topic: Good Mathematica Books?
Replies: 4
Views: 66618

Good Mathematica Books?

<r>For a general introduction there is "The Mathematica Book" that is included completely in both the program's help and the online documentation. I recommend reading it sequentially. I don't really know a better resource. Most books I've seen are dumbed down versions of this. There are also the mor...
by benczur
December 18th, 2007, 12:34 pm
Forum: Brainteaser Forum
Topic: Random Intervals
Replies: 44
Views: 69546

Random Intervals

<t>QuoteOriginally posted by: ChicagoGuyWhen I say (x, 2n+1) is good I mean that the resulting configuration has at least one interval intersecting all others, not that (x, 2n+1) is the interval intersecting all others. That indeed eliminates my second remark. However you still neglect the (N+2) con...
by benczur
December 17th, 2007, 11:32 pm
Forum: Brainteaser Forum
Topic: Random Intervals
Replies: 44
Views: 69546

Random Intervals

<t>QuoteOriginally posted by: tetrabitThere is a solution in Peter Winkler's Mathematical Puzzles: A Connoisseur's Collection. It's a bit messy though, don't know if there is an elegant solution.I've checked this solution on pp.40-42 in the book (hint: you can use amazon's search inside). It is a ni...
by benczur
December 17th, 2007, 7:59 pm
Forum: Brainteaser Forum
Topic: Random Intervals
Replies: 44
Views: 69546

Random Intervals

<t>Hi ChicagoGuy,I do have several issues with your proof and as a result I do not think it is correct:* first, you are not generating all configurations for N+2; the ones with the interval {2n+1,2n+2} are missing. You can get away with it if you are counting good ones, like in my proof, but not if ...
by benczur
December 17th, 2007, 6:53 pm
Forum: Brainteaser Forum
Topic: Random Intervals
Replies: 44
Views: 69546

Random Intervals

<t>QuoteOriginally posted by: MCarreiraOk, I see the illustration of your adding method, but how do you prove that the proportion between good and partitions is constant ?For n=4, we have the 2 patterns you described, but for n=6, your patterns are sometimes simmetric (2nd row 1st column with 1st ro...
by benczur
December 16th, 2007, 11:04 pm
Forum: Brainteaser Forum
Topic: Random Intervals
Replies: 44
Views: 69546

Random Intervals

Here are the figures for going from 4 to 6. For 4 points there are 2 good configurations/partitions. For 6 points, there are 10 good ones, five times more.The thick line is the first interval intersecting all others, the maroon ones are the intervals added when going from 4 to 6.