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Next Number

  1. May 18, 2005 #1
    Which number is next in this series:

    10, 4, 3, 11, 15...?

    a. 14
    b. 1
    c. 17
    d.12


    Hint: Not Math Related
     
  2. jcsd
  3. May 18, 2005 #2
    The pattern is this: number A, two numbers that are 1 in distance that decrease, one number 1 in distance from number A that increases, then two more numbers that are 1 in distance that decrease.

    The answer is a, 14.
     
  4. May 18, 2005 #3
    No, not really. Although the answer is correct, the reasoning behind it is incorrect. If you spell out each letter you can notice that for each number the number of letters increase by 1.
     
  5. May 19, 2005 #4
    can it be 14???
     
  6. May 19, 2005 #5
    lol..I got it in mathematical way. 10+11 = 21, 4+15 = 19 so 3+? = 17
     
  7. May 19, 2005 #6

    DaveC426913

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    Gold Member

    Wow. Cool. 3 right answers, with 3 completely independent rationales for reaching it.
     
  8. May 19, 2005 #7

    Alkatran

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    Correct answers are: a, b, c or d.

    If I knew how to use lagrange to make polynomials to fit those points I'd prove it, too.
     
  9. May 19, 2005 #8
    Its easier than that Alkatran:

    The polynomial [itex] y = (x - 10)(x - 4)(x - 3)(x - 11)(x - 15)(x - 14)[/itex] has zeros 10, 4, 3, 11, 15, and 14. This justifies the answer a. 14.

    The polynomial [itex] y = (x - 10)(x - 4)(x - 3)(x - 11)(x - 15)(x - 1)[/itex]has zeros 10, 4, 3, 11, 15, and 1. This justifies the answer b. 1.

    The polynomial [itex] y = (x - 10)(x - 4)(x - 3)(x - 11)(x - 15)(x - 17)[/itex] has zeros 10, 4, 3, 11, 15, and 17. This justifies the answer c. 17.

    The polynomial [itex] y = (x - 10)(x - 4)(x - 3)(x - 11)(x - 15)(x - 12)[/itex] has zeros 10, 4, 3, 11, 15, and 12. This justifies the answer d. 12.

    However, the correct answer to the puzzle was not one of the choices. You see the polynomial [itex] y = (x - 10)(x - 4)(x - 3)(x - 11)(x - 15)(x - \pi)[/itex] has zeros 10, 4, 3, 11, 15, and [itex]\pi[/itex]. So there is no correct answer.
     
    Last edited: May 19, 2005
  10. May 19, 2005 #9
    This is the only one that makes sense to me.
    14
     
  11. May 19, 2005 #10
    Wow... It's amazing how many patterns and relationships you can find, and they are all valid. I got my answer the same way that z-component got his.
     
  12. May 19, 2005 #11
    I don't think anybody has a convincing stab at this puzzle (myself included). Solving a pattern requires that you find something that is obviously right. Just being able to construct something that fits the pattern isn't enough. It has to also be simple and clearly the intended answer. Only if the intended answer does not itself fit those criteria is the pattern flawed.
     
  13. May 19, 2005 #12
    Plus, aditya said this is NOT math-related. No polynomials allowed. That's not the real point of why the polynomial approach is not right, but it adds some extra irony.
     
  14. May 19, 2005 #13
    I agree. Finding a pattern may not mean that you've found the answer. I think this one was a pretty creative pattern.
     
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