Results 1 to 2 of 2

Thread: Am I correct?

  1. #1
    Senior Member I-Think's Avatar
    Joined
    Apr 2009
    Posts
    288

    Am I correct?

    Got a challenging question (for me) that I want to ensure that I am correct.

    Question
    The numbers 828 and 313 are 3-digit palindromes where 828-313=515 which is also a palindrome. How many pairs (a, b) of 3-digit palindromes are there with a>b and with a-b also a 3-digit palindrome?

    My Answer: 1980
    Reasoning
    Conditions
    1. For palindromes aba and cdc to for a palindrome, then b>d.
    2. To form a 3-digit palindrome, then a>1.

    So we check a case by case analysis, starting with a=9 and varying b $\displaystyle (0\leq{b}\leq{9})$
    Number: 909 919 929 939 .... 999
    Pairs: 8 16 24 32 .... 80

    Moving onto a=8
    Number: 808 818 828 ..... 898
    Pairs: 7 14 21 ..... 70

    And so on to a=2
    Number: 202 212 .... 292
    Pairs: 1 2 .... 10

    So we a pattern of
    8x(1+2+3+...+10) + 7x(1+2+3+...+10) + 1x(1+2+3+....10)
    This becomes
    (1+2+3+...+10)(1+2+3+...+8)=55x36
    Ans=1980

    So could someone please check this.
    Thanks
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Newbie
    Joined
    Jul 2019
    From
    Australia
    Posts
    1

    Re: Am I correct?

    Yes, you are correct. it is 1980.
    =(1+2+3+4+5+6+7+8+9+10)x(1+2++3+4+5+6+7+8)
    =55x36
    =1980

    And I think it is from the 2008 AMC exam paper.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 15
    Last Post: Jul 29th 2011, 01:39 AM
  2. Is this correct ?
    Posted in the Calculus Forum
    Replies: 3
    Last Post: Jul 16th 2010, 12:24 PM
  3. is this correct?
    Posted in the Math Topics Forum
    Replies: 1
    Last Post: Apr 24th 2009, 10:34 AM
  4. Is this correct
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: Mar 17th 2009, 05:43 AM
  5. is this correct?
    Posted in the Calculus Forum
    Replies: 2
    Last Post: Jul 1st 2008, 11:00 PM

Search Tags


/mathhelpforum @mathhelpforum