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Math Help - Replacing Numbers

  1. #1
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    Arrow Replacing Numbers

    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 other tow. This process is repeated a number of times.

    Gerry wants to get the number 2010 from as many starting triples a,a,a as possible. One way of couse is to start with 2010, 2010,2010. What are all the other ways?

    Thank you for you help!!
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  2. #2
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    2,2,2
    3,2,2
    3,4,2
    5,4,2
    5,6,2
    7,6,2
    7,8,2
    .....
    2009,2008,2
    2009,2010,2

    Note: you should specify that opening integers > 1
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  3. #3
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    Thanks bro!
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  4. #4
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    Arrow

    Is 2,2,2 the only way to get 2010?
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  5. #5
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    Quote Originally Posted by GuMing View Post
    Is 2,2,2 the only way to get 2010?
    No. Also 8,8,8 and 42,42,42 and 50,50,50 and 288,288,288 ; that's all.

    Here's 288:
    288,288,288
    575,288,288
    575,862,288
    1149,862,288
    1149,1436,288
    1723,1436,288
    1723,2010,288
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  6. #6
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    Thanks!
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  7. #7
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    Arrow

    Another problem.
    Gemma started with 2,2,2 and tried to get to 17,75,91 but without success. Is it possible to get 17,75,91 from 2,2,2?
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