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by Anonymous on March 8th, 2010

Anonymous

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Help answer this question below.

A Palindrome Number is a number that has symetric digits; that is if you reverse the order of the digits you get the same number.

ex: 786687 is a Palindrome. 54345 is a Palindrome. 787878 is NOT a Palindrome.
Prove that all 6 digit Palindromes are in fact mulitples of 11.
(in fact any even digit Palindrome is a multiples of 11)

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Answers. 1 helpful answer below.

  • by TWA on March 8th, 2010

    TWA

    First, break down your digits into their own variables. let's take 123321 for example.
    f + e + d + c+ b + a = 123321
    f=100000
    e=20000
    d=3000
    c=300
    b=20
    a=1

    Since we're dealing with palindromes, find the relationship between the reflected variable:
    100,000 = 1 * 100,000, so f = 100,000a
    20000 = 20*1000, so e = 1000b
    3000 = 300*10, so d = 10c

    Using the reflexive property, we can safely say that
    f+e+d+c+b+a = 100000a +1000b + 10c +c+b+a

    You could simplify that statement by adding like variables:
    100001a + 1001b +11c =f+e+d+c+b+a

    See anything similar about those numbers? They're divisible by 11:
    11(9091a + 91b+c) = f+e+d+c+b+a

    There, I did your homework for you. Only because if someone else does your homework for you, you're more likely to fail your tests. And that thought brings a smile to my face.

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