Results 1 to 5 of 5

Math Help - Sum of 3 digits

  1. #1
    Senior Member DivideBy0's Avatar
    Joined
    Mar 2007
    From
    Melbourne, Australia
    Posts
    432

    Sum of 3 digits

    In how many ways can one select 3 different integers ranging from 1 to 30 inclusive so that their sum is a multiple of 3 (order of selection does not matter)?

    (A) 3160
    (B) 1360
    (C) 1240
    (D) 1353
    (E) 3240

    I don't know where to begin with this one, yeah... I'm pretty much stumped.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,965
    Thanks
    1785
    Awards
    1
    Please tell us what sorts of tools you have to work with. That is, what topics are surrounding this problem? How are you expected to work it? I ask because I know the correct answer but I had to use the programming ability of a computer algebra system to solve it. I have not found any way to model this problem using counting techniques.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,909
    Thanks
    772
    Hello, DivideBy0!

    I have an approach to this problem, but I don't know if it is valid.
    . . If I'm wrong, I hope someone can explain it.


    In how many ways can one select 3 different integers ranging from 1 to 30 inclusive
    so that their sum is a multiple of 3 (order of selection does not matter)?

    . . (A) 3160 . . (B) 1360 . . (C) 1240 . . (D) 1353 . . (E) 3240

    There are:
    30C3 = 4060 ways to select 3 distinct integers from 1 to 30.

    The sums will range from: .1 + 2 + 3 .= .6 .to .28 + 29 + 30 .= .87

    Here's where I'm being quite daring . . .
    . . I assume that one-third of the sums are divisible by 3.

    And 4060 3 is suspiciously close to answer (D): 1353.

    Follow Math Help Forum on Facebook and Google+

  4. #4
    Senior Member DivideBy0's Avatar
    Joined
    Mar 2007
    From
    Melbourne, Australia
    Posts
    432
    Sorry I didn't reply to your post Plato, the question is from a grade 9-10 competition paper, so the questions are from a wide range of topics.

    Quote Originally Posted by Soroban View Post
    Hello, DivideBy0!

    I have an approach to this problem, but I don't know if it is valid.
    . . If I'm wrong, I hope someone can explain it.


    There are: 30C3 = 4060 ways to select 3 distinct integers from 1 to 30.

    The sums will range from: .1 + 2 + 3 .= .6 .to .28 + 29 + 30 .= .87

    Here's where I'm being quite daring . . .
    . . I assume that one-third of the sums are divisible by 3.

    And 4060 3 is suspiciously close to answer (D): 1353.
    That's a very elegant way of looking at the problem, and it's very close to the actual answer, which the answers give as (B): 1360. Nice try Soroban.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,965
    Thanks
    1785
    Awards
    1

    Here the way I did using the Boolean capabilities of a simple CAS.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. How many digits?
    Posted in the Number Theory Forum
    Replies: 6
    Last Post: April 19th 2011, 12:51 PM
  2. Replies: 7
    Last Post: November 28th 2010, 10:22 PM
  3. Digits
    Posted in the Algebra Forum
    Replies: 2
    Last Post: March 23rd 2010, 06:11 AM
  4. Sum of the digits
    Posted in the Algebra Forum
    Replies: 1
    Last Post: April 7th 2008, 04:50 AM
  5. Replies: 2
    Last Post: April 3rd 2007, 01:31 PM

Search Tags


/mathhelpforum @mathhelpforum