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Math Help - Urgent algebra homework! Xmas stuff... :D

  1. #1
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    Urgent algebra homework! Xmas stuff... :D

    Despite the season being over I am still left puzzled over this problem.

    The following questions are related to the popular Christmas song "The Twelve Days of Christmas".

    We all know it's fairly simple to figure out the amount of presents found over the twelve days of Christmas. It is 364 presents.

    How many ways did you find to solve for 364 presents?

    Tough what about Twelve Days of Christmas? How many presents would we receive then?
    And the toughest of them all THE nth day of Christmas? How on Earth are we supposed to explain and work out the nth day of Christmas?

    Help needed.
    Thanks!
    Last edited by chocole; January 7th 2008 at 10:36 AM.
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  2. #2
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    Quote Originally Posted by chocole View Post
    Despite the season being over I am still left puzzled over this problem.

    The following questions are related to the popular Christmas song "The Twelve Days of Christmas".

    We all know it's fairly simple to figure out the amount of presents found over the twelve days of Christmas. It is 364 presents.

    How many ways did you find to solve for 364 presents?

    Tough what about Twelve Days of Christmas? How many presents would we receive then?
    And the toughest of them all THE nth day of Christmas? How on Earth are we supposed to explain and work out the nth day of Christmas?

    Help needed.
    Thanks!

    Tiina
    Maybe I am not familiar with the version you know. If you get 1 present on the first day, 2 presents on the 2nd day, and n presents on the nth day, then your total is:

    \sum_{i=0}^n i = \frac{n(n+1)}{2}
    Last edited by colby2152; January 7th 2008 at 10:32 AM. Reason: fixed subscript
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  3. #3
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    Quote Originally Posted by colby2152 View Post
    Maybe I am not familiar with the version you know. If you get 1 present on the first day, 2 presents on the 2nd day, and n presents on the nth day, then your total is:

    \sum_0^n i = \frac{n(n+1)}{2}
    The problem states how many presents would be received over any other number (n) of days.

    Could you explain your answer to me?

    I am brain dead. I've never been this stuck... on this kind of problem. XD
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  4. #4
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    Quote Originally Posted by chocole View Post
    The problem states how many presents would be received over any other number (n) of days.

    Could you explain your answer to me?

    I am brain dead. I've never been this stuck... on this kind of problem. XD
    The formula for the sum of an arithmetic series is:

    S_{n} = \frac{n}{2} \left( 2a + (n - 1)d \right)

    a = 1 and d = 1

    So:

    S_{n} = \frac{n}{2} \left( 2 + (n - 1) \right)

    S_{n} = \frac{n}{2} \left( n + 1 \right)

    S_{n} = \frac{n^2 + n}{2}

    Where n = the number of days.

    So on the 1st day you would have 1 present, on the 2nd day, you would receive 3 presents, etc...
    Last edited by janvdl; January 7th 2008 at 10:51 AM. Reason: Sorry i misunderstood the lyrics... :-D
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  5. #5
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    Hello, chocole!

    The following questions are related to the Christmas song "The Twelve Days of Christmas".

    We all know how to figure out the number of presents given over the 12 days.
    It is 364 presents.

    How many ways did you find to solve for 364 presents?

    \begin{array}{cccc}\text{Day} & & \text{Presents} \\<br />
1 &1 & 1  \\ <br />
2 & 1+2 & 3 \\<br />
3 & 1+2+3 & 6 \\<br />
4 & 1+2+3+4 & 10 \\<br />
\vdots & \vdots & \vdots<br />
\end{array} . These are "triangular numbers."


    On the n^{th} day, my true love gave to me: . \frac{n(n+1)}{2} gifts.


    By the n^{th} day, my true love gave to me a total of:

    . . \sum^n_{k=1}\frac{k(k+1)}{2} \;=\;\frac{n(n+1)(n+2)}{6} gifts.

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