Results 1 to 6 of 6

Math Help - Extremely interesting number theory problem?

  1. #1
    Super Member fardeen_gen's Avatar
    Joined
    Jun 2008
    Posts
    539

    Extremely interesting number theory problem?

    A leaf is torn from a novel. The sum of the numbers on the remaining pages is 15000. What are the page numbers on the torn leaf?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by fardeen_gen View Post
    A leaf is torn from a novel. The sum of the numbers on the remaining pages is 15000. What are the page numbers on the torn leaf?
    25 and 26

    RonL
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member fardeen_gen's Avatar
    Joined
    Jun 2008
    Posts
    539
    I know the answers.
    (i found it out using the n(n+1)/2 formula and finding n for 15000 ,which yielded a non-whole value, and finding sum for the next greater whole value. The sum obtained i.e 15051 minus 15000 yielded 51 and since the torn leaf has consecutive page numbers, i got 25 and 26)

    I would say the above method is extremely crude and wouldn't be accepted as a solution at all.Does anybody know the proper solution to this problem using number theory(as the question was listed in a number theory question bank)??
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by fardeen_gen View Post
    I know the answers.
    (i found it out using the n(n+1)/2 formula and finding n for 15000 ,which yielded a non-whole value, and finding sum for the next greater whole value. The sum obtained i.e 15051 minus 15000 yielded 51 and since the torn leaf has consecutive page numbers, i got 25 and 26)

    I would say the above method is extremely crude and wouldn't be accepted as a solution at all.Does anybody know the proper solution to this problem using number theory(as the question was listed in a number theory question bank)??
    It is a perfectly acceptable method. There are no rules in number theory about what methods are acceptable. You suppose that the number of pages is N, and then you bound N by considering the greatest and least total that the missing leaf would contribute, and you find only one integer that satisfies the constraints)

    (not only does the removed leaf have one odd and one even number the odd number must be one less than the even.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Super Member fardeen_gen's Avatar
    Joined
    Jun 2008
    Posts
    539
    Thank you Captain Black. Are there other methods also?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Newbie
    Joined
    Nov 2008
    Posts
    1

    Smile by the same logic

    If n=174 ( no. of pages in the book) then the number on the torn leaf will be 112 and 113.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Number Theory problem
    Posted in the Number Theory Forum
    Replies: 15
    Last Post: June 29th 2010, 08:04 AM
  2. Replies: 2
    Last Post: December 18th 2008, 05:28 PM
  3. Extremely difficult number theory problem?
    Posted in the Number Theory Forum
    Replies: 2
    Last Post: November 8th 2008, 04:27 AM
  4. Number theory, prime numbers, interesting problem
    Posted in the Number Theory Forum
    Replies: 2
    Last Post: October 21st 2007, 01:23 AM
  5. Number Theory GCD Problem
    Posted in the Number Theory Forum
    Replies: 2
    Last Post: October 10th 2006, 04:59 PM

Search Tags


/mathhelpforum @mathhelpforum