1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Arrange the numbers 1 through 10 in the shape of a pyramid

  1. Feb 3, 2004 #1
    Arrange the numbers 1 through 10 in the shape of a pyramid (1 number at the peak, 2 numbers in the next row down, 3 in the next row, and 4 in the bottom row). The numbers must be arranged such that each number is equal to the difference of the two numbers directly below it. For example, if 5 and 1 are next to each other in the same row, then 4 must be placed on top of them.
     
  2. jcsd
  3. Feb 3, 2004 #2
    3
    7 4
    2 9 5
    8 10 1 6
    It represents a pyramid, though I'm unable to give to it a pyramidal shape
     
  4. Feb 3, 2004 #3

    NateTG

    User Avatar
    Science Advisor
    Homework Helper

    It looks good, but if you're reall picky you can use the code tag for fixed spacing

    Code (Text):

       3
      7 4
     2 9 5
    8 A 1 6
     
    I wonder if the solution is unique. Apparently not:

    Code (Text):

       3
      2 5
     7 9 4
    8 1 A 6
     
     
    Last edited: Feb 3, 2004
  5. Feb 3, 2004 #4

    chroot

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    There are eight solutions:

    {3, 2, 5, 7, 9, 4, 8, 1, 10, 6},
    {3, 4, 7, 5, 9, 2, 6, 1, 10, 8},
    {3, 5, 2, 4, 9, 7, 6, 10, 1, 8},
    {3, 7, 4, 2, 9, 5, 8, 10, 1, 6},
    {4, 1, 5, 6, 7, 2, 9, 3, 10, 8},
    {4, 2, 6, 5, 7, 1, 8, 3, 10, 9},
    {4, 5, 1, 2, 7, 6, 8, 10, 3, 9},
    {4, 6, 2, 1, 7, 5, 9, 10, 3, 8}

    - Warren
     
  6. Feb 4, 2004 #5
    For 1 level, there are 4 solutions:

    2 / 1 3
    2 / 3 1
    1 / 2 3
    1 / 3 2

    3 always appears on the bottom.

    For 2 levels, there are 6 solutions:

    2 / 3 5 / 4 1 6
    2 / 5 3 / 6 1 4
    1 / 3 4 / 5 2 6
    1 / 4 3 / 6 2 5
    3 / 4 1 / 2 6 5
    3 / 1 4 / 5 6 2

    6 always appears on the bottom. 5 and 4 appear on the bottom two levels, with only one of these at the highest.

    I trust there are no more than 8 solutions for 3 levels:

    3 / 4 7 / 5 9 2 / 6 1 A 8
    3 / 7 4 / 2 9 5 / 8 A 1 6
    3 / 2 5 / 7 9 4 / 8 1 A 6
    3 / 5 2 / 4 9 7 / 6 A 1 8
    4 / 2 6 / 5 7 1 / 8 3 A 9
    4 / 6 2 / 1 7 5 / 9 A 3 8
    4 / 1 5 / 6 7 2 / 9 3 A 8
    4 / 5 1 / 2 7 6 / 8 A 3 9

    10 always appears on the bottom. 8 and 9 appear on the bottom two levels. (In fact 8 is always on the bottom.) 5, 6, and 7 appear on the bottom three levels, with only one of these at the highest.

    What a great way to waste time...
     
  7. Feb 4, 2004 #6
    meteor with the point, good work chroot and davilla!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Arrange the numbers 1 through 10 in the shape of a pyramid
  1. I want to be number 1 (Replies: 15)

  2. Base 10 numbering system (Replies: 26)

Loading...