Results 1 to 4 of 4

Thread: Elementary Math Problem

  1. March 23rd 2009, 11:36 AM #1
    phillyfan09
    phillyfan09 is offline
    Newbie
    Joined
    Feb 2009
    Posts
    12

    Exclamation Elementary Math Problem

    How many cubes are in the 10th collection of cubes in this sequence?

    1st- 1 cube
    2nd- 4 cubes
    3rd- 10 cubes.....
    l
    l
    l
    10th- ? cubes

    Any help appreciated!
    Follow Math Help Forum on Facebook and Google+
  2. March 23rd 2009, 12:38 PM #2
    Grandad
    Grandad is offline
    MHF Contributor
    Grandad's Avatar
    Joined
    Dec 2008
    From
    South Coast of England
    Posts
    2,570

    Tetrahedral numbers

    Hello phillyfan09
    Quote Originally Posted by phillyfan09 View Post
    How many cubes are in the 10th collection of cubes in this sequence?

    1st- 1 cube
    2nd- 4 cubes
    3rd- 10 cubes.....
    l
    l
    l
    10th- ? cubes

    Any help appreciated!
    The sequence 1, 4, 10, ... is sometimes called Tetrahedral Numbers. Here's the answer to your question: Tetrahedral number - Wikipedia, the free encyclopedia.

    Grandad
    Follow Math Help Forum on Facebook and Google+
  3. March 23rd 2009, 05:04 PM #3
    Soroban
    Soroban is offline
    Super Member
    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,242
    Thanks
    370
    Hello, phillyfan09!

    Where did this problem come from?
    It doesn't give enough information to allow us a good guess.

    Lucky for us, Grandad recognized the sequence.

    How many cubes are in the 10th collection of cubes in this sequence?

    . . \begin{array}{cc} <br /> \text{1st} & \text{1 cube} \\<br /> \text{2nd} & \text{4 cubes} \\<br /> \text{3rd} & \text{10 cubes} \\<br /> \vdots & \vdots \\<br /> \text{10th} & \text{? cubes} \end{array}

    Imagine a display of oranges, stacked in a triangular pyramid (tetrahedron).
    . . Each horizontal level is an equilateral triangle.

    \begin{array}{ccccc}\text{Level} & \text{array} & \text{count} & \text{Total} \\ \hline \\[-4mm] 1 & o & 1 & 1\\ 2 & \begin{array}{c}o\\ [-3mm] oo\end{array} & 3 & 4\\ 3 & \begin{array}{c}o \\ [-3mm] oo \\[-3mm] ooo\end{array} & 6 & 10 \\ 4 & \begin{array}{c} o \\[-3mm] oo\\[-3mm]ooo\\[-3mm]oooo\end{array} & 10 & 20 \\\vdots & \vdots & \vdots & \vdots \end{array}


    And we want the 10th Total on this list.


    You can crank out the numbers yourself, or you can use this formula:

    . . T(n) \;=\;\frac{n(n+1)(n+2)}{6}


    ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~


    By the way, this formula answers the question:

    How many gifts did My True Love Give To Me
    . . during the Twelve Days of Christmas?

    . . \begin{array}{cccc}\text{Day} & \text{Gifts} & \text{Number} \\ \hline 1 & 1 & 1 \\ 2 &1+2 & 3 \\ 3 & 1+2+3 & 6 \\ 4 & 1+2+3+4 & 10 \\ \vdots & \vdots & \vdots \\ 12 & 1+2+\hdots+12 & 78 \\ \hline & \text{Total} & {\color{blue}364}\end{array}
    Follow Math Help Forum on Facebook and Google+
  4. March 24th 2009, 07:16 AM #4
    phillyfan09
    phillyfan09 is offline
    Newbie
    Joined
    Feb 2009
    Posts
    12
    Problem came from a college level elementary course...I believe professor made it up.

    Thanks!
    Follow Math Help Forum on Facebook and Google+
« Condition for real roots | Help required »

Similar Math Help Forum Discussions

  1. two elementary number theory problem:
    Posted in the Number Theory Forum
    Replies: 8
    Last Post: October 12th 2010, 05:13 AM
  2. elementary kinematics problem
    Posted in the Advanced Applied Math Forum
    Replies: 0
    Last Post: March 22nd 2010, 03:34 AM
  3. Math Exam tomorrow (elementary algebra) help :(
    Posted in the Algebra Forum
    Replies: 6
    Last Post: December 16th 2009, 03:07 AM
  4. elementary math problems need answer
    Posted in the Math Topics Forum
    Replies: 3
    Last Post: May 8th 2009, 02:58 AM
  5. Elementary set theory problem
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: April 1st 2008, 03:48 PM

Search Tags


/mathhelpforum @mathhelpforum