Page 41 of 43 FirstFirst ... 313940414243 LastLast
Results 601 to 615 of 645

Thread: The Maths Thread

  1. #601
    International Coach
    Suicide Bob Champion!
    Join Date
    Aug 2010
    Location
    Not really needed on CW
    Posts
    12,754
    Quote Originally Posted by vcs View Post
    Ugh.. yes. This is getting a bit complicated. Will get some sleep, clear my mind and think about it again tomorrow. Same for your reply in the programming thread as well, Ankit.
    Quote Originally Posted by silentstriker View Post
    I'm massively sleep deprived but: 0. Monkeys, Shakespeare, etc.

    Right?
    Quote Originally Posted by weldone View Post
    In fact, for any x where 0<x<1, if you replace 3/4 by x and 1/4 by (1-x) in the original problem, then also p will come out as 1 from the equation I think. I'm also sleep-deprived, so not putting an effort to solve that generic one lol.
    Quote Originally Posted by weldone View Post
    I'll try that tommorrow maybe (assuming it doesn't need your continuous geometric algebra or stuff sounding similar to that ). Too sleepy now...
    Quote Originally Posted by nightprowler10 View Post
    It's 2am so I might be missing something, but I get ln(2/5) evaluating the attached problem but the correct answer apparently is (1/3)ln(5/2). What the hell am I missing?

    EDIT: oh god, ignore me.
    worrying trend amongst our numb3r crunchers

  2. #602
    International Coach uvelocity's Avatar
    Join Date
    Sep 2011
    Location
    seamy road
    Posts
    11,865
    Quote Originally Posted by sledger View Post
    I just love all kinds of balls.

  3. #603
    International Coach
    Suicide Bob Champion!
    Join Date
    Aug 2010
    Location
    Not really needed on CW
    Posts
    12,754
    slightly ashamed that i know what that means and even laughed

  4. #604
    International Coach KiWiNiNjA's Avatar
    Join Date
    Feb 2007
    Location
    In the kitchen
    Posts
    10,601
    Window!!


  5. #605
    International Captain wellAlbidarned's Avatar
    Join Date
    Jan 2011
    Location
    away from the palms
    Posts
    6,400
    Now here's some **** I understand
    Exit pursuing a beer

  6. #606
    International Captain wellAlbidarned's Avatar
    Join Date
    Jan 2011
    Location
    away from the palms
    Posts
    6,400
    Quote Originally Posted by nightprowler10 View Post
    It's 2am so I might be missing something, but I get ln(2/5) evaluating the attached problem but the correct answer apparently is (1/3)ln(5/2). What the hell am I missing?

    EDIT: oh god, ignore me.
    aha we've all been there. The little things.

  7. #607
    International Captain weldone's Avatar
    Join Date
    Jan 2008
    Location
    Kolkata->Mumbai->London
    Posts
    6,177
    Prove that two consecutive numbers from Fibonacci Series are always relatively prime.
    "I want to raise my hand and say one thing. Those who complain about my love for the game or commitment to the game are clueless. These are the only 2 areas where I give myself 100 out of 100."
    - Sachin Tendulkar, as told in an interview published in Bengali newspaper Anandabazar Patrika after his 100th International century (translated by weldone)

  8. #608
    Global Moderator Spark's Avatar
    Join Date
    Feb 2010
    Location
    A Blood Rainbow
    Posts
    32,623
    by contradiction and induction.

    let f(n), f(n+1) be the nth fibonacci number for some integer n. suppose n=1. well... that's sort of trivial, i won't bother.

    suppose true for some n=k ie. f(k) and f(k+1) are coprime.

    suppose f(k+1) and f(k+2) are not coprime ie. there exists some non-trivial divisor d of both.
    but f(k) = f(k+2) - f(k+1) so f(k) is also divisible by d. but this means that f(k), f(k+1) are not coprime - contradiction, qed, done.
    + time's fickle card game ~ with you and i +


    get ready for a broken ****in' arm

  9. #609
    International Captain ankitj's Avatar
    Join Date
    Jul 2010
    Location
    Hyderabad India
    Posts
    6,183
    Neat. Loved it.

  10. #610
    International Captain ankitj's Avatar
    Join Date
    Jul 2010
    Location
    Hyderabad India
    Posts
    6,183
    Another question related to fibonacci numbers (I was asked this in an interview): What does the ratio of consecutive fibonacci number, f(k+1)/f(k) converge to as we go to as k->∞?

    The part that was relatively easy was to find that ratio assuming convergence. But I don't known how to show there will be convergence in the first place. That will probably require university level calculus which I don't much remember (for every epsilon ε there exists a delta δ etc...)

    EDIT: For limit of a sequence, you don't have δ but N.
    Last edited by ankitj; 05-03-2013 at 06:20 AM.

  11. #611
    International Captain weldone's Avatar
    Join Date
    Jan 2008
    Location
    Kolkata->Mumbai->London
    Posts
    6,177
    Quote Originally Posted by Spark View Post
    by contradiction and induction.

    let f(n), f(n+1) be the nth fibonacci number for some integer n. suppose n=1. well... that's sort of trivial, i won't bother.

    suppose true for some n=k ie. f(k) and f(k+1) are coprime.

    suppose f(k+1) and f(k+2) are not coprime ie. there exists some non-trivial divisor d of both.
    but f(k) = f(k+2) - f(k+1) so f(k) is also divisible by d. but this means that f(k), f(k+1) are not coprime - contradiction, qed, done.
    Exactly.

    Simple, isn't it? I've asked that question to 3 people while interviewing them yesterday. None of them got it right without any hint. (One guy cracked it after I suggested him to approach it through method of induction.)
    Last edited by weldone; 05-03-2013 at 08:20 AM.

  12. #612
    International Captain weldone's Avatar
    Join Date
    Jan 2008
    Location
    Kolkata->Mumbai->London
    Posts
    6,177
    Quote Originally Posted by 8ankitj View Post
    Another question related to fibonacci numbers (I was asked this in an interview): What does the ratio of consecutive fibonacci number, f(k+1)/f(k) converge to as we go to as k->∞?

    The part that was relatively easy was to find that ratio assuming convergence. But I don't known how to show there will be convergence in the first place. That will probably require university level calculus which I don't much remember (for every epsilon ε there exists a delta δ etc...)

    EDIT: For limit of a sequence, you don't have δ but N.
    It's very easy after assuming convergence.

    f(k+1)/f(k) = {f(k)+f(k-1)}/f(k) = 1 + f(k-1)/f(k)
    So, if the answer is x then x ~ (1 + 1/x)
    => x^2-x-1 = 0

    Solving this quadratic and ignoring the value that is less than 1, we get
    x = sqrt(5)/2 +0.5

  13. #613
    International Captain ankitj's Avatar
    Join Date
    Jul 2010
    Location
    Hyderabad India
    Posts
    6,183
    Quote Originally Posted by weldone View Post
    Exactly.

    Simple, isn't it? I've asked that question to 3 people while interviewing them yesterday. None of them got it right without any hint. (One guy cracked it after I suggested him to approach it through method of induction.)
    Good enough performance considering interview pressure, isn't it? I try to keep interview questions somewhat stress free and non-trick kind. Here's a question I have been asking for data analyst kind of roles:

    Probability of observing an accident in one hour period on an accident prone bridge is 10%. What is the probability of observing an accident in two hour period?

    Don't mind if the candidate answers it after some hints. Is that too lenient?

  14. #614
    International Captain weldone's Avatar
    Join Date
    Jan 2008
    Location
    Kolkata->Mumbai->London
    Posts
    6,177
    Quote Originally Posted by 8ankitj View Post
    probability of observing an accident in one hour period on an accident prone bridge is 10%. What is the probability of observing an accident in two hour period?
    0.19?

  15. #615
    Global Moderator Spark's Avatar
    Join Date
    Feb 2010
    Location
    A Blood Rainbow
    Posts
    32,623
    yeah that's just 1 - 0.9^2 innit?

Page 41 of 43 FirstFirst ... 313940414243 LastLast


Thread Information

Users Browsing this Thread

There are currently 1 users browsing this thread. (0 members and 1 guests)

Similar Threads

  1. Tech Geeks Thread
    By SupaFreak2005 in forum Off Topic
    Replies: 233
    Last Post: 03-11-2012, 03:15 PM
  2. *Nikhil Hearing* Details Thread
    By lord_of_darkness in forum Cricket Web XI
    Replies: 329
    Last Post: 17-12-2004, 03:21 PM
  3. **Official** South Africa in India Thread
    By Neil Pickup in forum Cricket Chat
    Replies: 453
    Last Post: 08-12-2004, 07:26 AM
  4. *Official* India in Australia Thread
    By Craig in forum Cricket Chat
    Replies: 2652
    Last Post: 08-01-2004, 07:00 PM
  5. *Official* West Indies in Zimbabwe Thread
    By Mr Mxyzptlk in forum Cricket Chat
    Replies: 554
    Last Post: 01-12-2003, 03:11 AM

Posting Permissions

  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts
  •