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  1. #1
    Senior Member Ming's Avatar
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    Default Solve this Math Problem? (With Proof!)

    Three identical integers greater than 1 are written on a board. One of the numbers is rubbed off and replaced by a number which is one less than the sum of the two. This process is repeated a number of times. The number rubbed off is always chosen so that it is different from its replacement.

    Adam wants to get the number 2010 from as many starting triples a, a, a as possible. One way (obviously) is to start with 2010, 2010, 2010. What are all the other ways?

  2. #2
    lab rat extraordinaire CrystalViolet's Avatar
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    Are you trying to get some one to do your home work for you ?Just teasing, LOL
    Currently submerged under an avalanche of books and paper work. I may come back up for air from time to time.
    Real life awaits and she is a demanding mistress.

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  3. #3
    Don't pet me. JAVO's Avatar
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    Adam should really find a more interesting and useful problem to solve.

  4. #4
    Senior Member Ming's Avatar
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    Quote Originally Posted by FireyPheonix View Post
    Are you trying to get some one to do your home work for you ?Just teasing, LOL
    Maybe, maybe.

    I was just interested. Testing the NT's intelligence mainly.

  5. #5
    Senior Member Lateralus's Avatar
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    Default

    I'm not sure I even understand the problem.

    2a-1=2010 a=1005.5 (not an integer)
    3a-2=2010 a=670.666 (not an integer)
    4a-3=2010 a=503.25 (not an integer)
    5a-4=2010 a=402.8 (not an integer)
    6a-5=2010 a=335.8333 (not an integer)
    7a-6=2010 a=288
    8a-7=2010 a=252.125 (not an integer)
    9a-8=2010 a=224.2222 (not an integer)
    10a-9=2010 a=201.9 (not an integer)
    11a-10=2010 a=183.6363 (not an integer)
    12a-11=2010 a=168.4166 (not an integer)
    13a-12=2010 a=155.538 (not an integer)
    ...

    Do I really have to keep doing this?
    "We grow up thinking that beliefs are something to be proud of, but they're really nothing but opinions one refuses to reconsider. Beliefs are easy. The stronger your beliefs are, the less open you are to growth and wisdom, because "strength of belief" is only the intensity with which you resist questioning yourself. As soon as you are proud of a belief, as soon as you think it adds something to who you are, then you've made it a part of your ego."

  6. #6
    Senior Member forzen's Avatar
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    Same here, I don't think I even understood the problem.

    2009 - n, 0002 + n, 2010

    1<n<2008
    This post grammatical errors had been intentionally left uncorrected.

  7. #7
    Senior Member Ming's Avatar
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    Alright, I'll try to explain what it means.

    So you choose an integer that is greater than one, and call it a.

    You repeat it 3 times, and write it on the blackboard.

    You rub out one of the integers that you have written, and replace it with the one less than SUM the two remaining integers.

    For example, I start with 3,3,3.

    I rub out a 3.

    I'm left with 3,_,3.

    I fill in the blank with one less than the sum of these two. (Which is 3+3-1 = 5)

    3,5,3.

    From that point onwards, I take away the 3 again.

    _,5,3.

    I get 7,5,3. (Since 5+3-1 = 7)

    And etc, etc...

    Until one or more of the numbers is 2010.

    The question is asking how many of a as an integer can we have? Basically how many a,a,a possibilities that are integers can we have so that one of the numbers end up to be 2010.

    Get it?

  8. #8
    Senior Member InsatiableCuriosity's Avatar
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    Is this not the basis of the Fibonaci Sequence?
    "Study hard what interests you the most in the most undisciplined, irreverent and original manner possible."
    — Richard P. Feynman

    "Never tell a person a thing is impossible. G*d/the Universe may have been waiting all this time for someone ignorant enough of the impossibility to do just that thing."
    author unknown

  9. #9
    Senior Member forzen's Avatar
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    Quote Originally Posted by Ming View Post
    Three identical integers greater than 1 are written on a board. One of the numbers is rubbed off and replaced by a number which is one less than the sum of the two. This process is repeated a number of times. The number rubbed off is always chosen so that it is different from its replacement.

    Adam wants to get the number 2010 from as many starting triples a, a, a as possible. One way (obviously) is to start with 2010, 2010, 2010. What are all the other ways?
    I read the bold part wrong, because if you do 3,3,3 it would give you 3,5,3.

    3+3=6

    One less then the sum of the two is 5.
    Last edited by forzen; 05-29-2010 at 08:10 AM. Reason: Which is what you're trying to say. har har.
    This post grammatical errors had been intentionally left uncorrected.

  10. #10
    Senior Member Lateralus's Avatar
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    The series is ba-b+1=2010 which gives you b=2009/(a-1)

    It looks like you're asking for the factors of 2009 and adding 1 to them.

    8, 42, 50, 288
    "We grow up thinking that beliefs are something to be proud of, but they're really nothing but opinions one refuses to reconsider. Beliefs are easy. The stronger your beliefs are, the less open you are to growth and wisdom, because "strength of belief" is only the intensity with which you resist questioning yourself. As soon as you are proud of a belief, as soon as you think it adds something to who you are, then you've made it a part of your ego."

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