Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

pythagoras123

  • 2 years ago

Three different integers from 1 to 11 are selected. In how many of these combinations of 3 numbers are their sums a multiple of 3?

  • This Question is Closed
  1. pythagoras123
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    how did you get 26? O_O

  2. pythagoras123
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    erm... no.

  3. inkyvoyd
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Gah, FFM, you just gave me another strange problem to think about. The sum of the fib numbers?

  4. dumbcow
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    the answer is 57 but i don't have a mathematical proof for you i used a computer to evaluate all possible cases

  5. anonymoustwo44
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @FoolForMath... Can I ask what combination of 3numbers is. does that mean order doesn't matter? or for instance, in this cause would 132 be same as 123?

  6. FoolForMath
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Btw what is the problem source?

  7. pythagoras123
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Homework

  8. pythagoras123
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    That's why I need an explanation not just an answer

  9. FoolForMath
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Competitive math probably IMO?

  10. pythagoras123
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    dunno, but looks like it

  11. dumbcow
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    the distribution is as follows for combinations that sum up to 6,9,12 ... 1+3+7+11+13+11+7+3+1

  12. FoolForMath
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @anonymoustwo44: As this is combination 1+2+3 is same as 2+1+3

  13. myko
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    you can try like that: the sum of numbers a,b,c is divisible by 3 if the sum of their digits is divisible by 3.

  14. anonymoustwo44
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @FoolForMath so the number 231 will be the same as the combination 321?

  15. myko
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    they bouth divisible by 3

  16. anonymoustwo44
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so are they the same combination?

  17. myko
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    what do you mean? the maximum sum to check in this case is: 11+10+9 = 30 (digits sum =3) you never even get to 123 or 321

  18. anonymoustwo44
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    never mind me :))

  19. Ishaan94
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 3

    Every number can be expressed as 3n, 3n+1,3n+2 Case1. 3n,3n,3n Case2. 3n, 3n+1,3n+2 Case3. 3n+2,3n+2,3n+2 Case 4. 3n+1,3n+1,3n+1 In the set {1,2,..,11} 3 (3n forms), 4-4 (3n+1 and 3n+2) 3c3 + 3c1*4c1*4c1 + 4c3 + 4c1 How about this? :D

  20. Ishaan94
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 3

    3c3 + 3c1*4c1*4c1 + 4c3 + 4c3

  21. Ishaan94
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 3

    did i miss something? some case?maybe

  22. Ishaan94
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 3

    myko?

  23. myko
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    just you have to be carefull with n=0.... wait checking...

  24. Ishaan94
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 3

    i only counted 3, for 3n forms {3,6,9}

  25. Ishaan94
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 3

    3n+1 3n+2 for n = 0 1 and 2

  26. myko
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    never mind, you mean other thing, sry

  27. myko
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    you right, good job

  28. sheg
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Ishaan is correct

  29. sheg
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Answer for this problem is 26

  30. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Ask a Question
Find more explanations on OpenStudy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.