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Math Help - Palindromes -

  1. #1
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    Palindromes -

    Hi MHF
    Here's my question:
    There are 90 four-digit palindromic numbers.
    How many of these four-digit palindromic numbers are divisible by 7.
    So i have no idea how to start or what to do, i'm unable to obtain a pattern of any sort, i assume there are 10 palindromes between each thousand number bracket (1000-1999, 2000-2999 etc)
    Last edited by 99.95; March 13th 2010 at 06:55 AM.
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  2. #2
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    Quote Originally Posted by 99.95 View Post
    Hi MHF
    Here's my question:
    There are 90 four-digit palindromic numbers.
    How many of these four-digit palindromic numbers are divisible by 7.
    So i have no idea how to start or what to do, i'm unable to obtain a pattern of any sort, i assume there are 10 palindromes between each thousand number bracket (1000-1999, 2000-2999 etc)
    Hello 99.95

    Yes there are "10 palindromes between each thousand number bracket 1000-1999, 2000-2999 etc"

    And also there are only two palindromes in each thousand number bracket for e.g 1001 & 1771, 2002 & 2772,.....9009 & 9779

    So in total it makes 9*2=18 four-digit palindromic numbers that are divisible by 7.

    Hope this helps
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    Yes that helps, but i would like to know how you found that there are only two palindromes in each thousand number bracket which are divisble by 7. is there some sort of rule/theorem, or did you happen to use trial and error (Tedious),,
    Thanks
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  4. #4
    Member u2_wa's Avatar
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    Quote Originally Posted by 99.95 View Post
    Yes that helps, but i would like to know how you found that there are only two palindromes in each thousand number bracket which are divisble by 7. is there some sort of rule/theorem, or did you happen to use trial and error (Tedious),,
    Thanks
    I did it with trial and error for 1000-2000 and than checked to confirm that there are two palindromes in each thousand number!
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