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Palindromic numbers

This is a discussion on Palindromic numbers within the General Discussions forums, part of the Community Boards category; I've been revisiting some of the Project Euler problems that I skipped because I wasn't motivated at the time =) ...

  1. #1
    Registered User Hodor's Avatar
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    Palindromic numbers

    I've been revisiting some of the Project Euler problems that I skipped because I wasn't motivated at the time =)

    Anyway, problem #4 is called "Largest palindrome product":

    A palindromic number reads the same both ways. The largest palindrome made from the product of two 2-digit numbers is 9009 = 91 * 99.
    Find the largest palindrome made from the product of two 3-digit numbers.
    Source: Problem 4 - Project Euler


    I have a solution and have calculated the largest products for the products of 2-, 3-, 4-, 5-, 6-, and 7-digit numbers. And I get the sequence below (starting from the largest for 4-digit numbers so I don't give the answer to the question from Project Euler.

    9999 * 9901 = 99000099
    99979 * 99681 = 9966006699
    999999 * 999001 = 999000000999
    9999979 * 9467731 = 94677111177649

    This sequence (of the results) doesn't seem to be a named sequence. Is it too boring? Surely there must be a sequence or related sequence... I'm sure there are more obscure sequences than this one that are listed on, for example, on oeis.org.

    My solution is still brute force and that makes me uneasy but I can't seem to get my lightbulb to light.

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    There exists a larger palindrome product of two 7-digit numbers:

    9998017 * 9997647 = 99956644665999

    8-digit:
    99999999 * 99990001 = 9999000000009999

    9-digit:
    999980347 * 999920317 = 999900665566009999

    10-digit:
    9999999999 * 9999900001 = 99999000000000099999
    Last edited by nonoob; 12-19-2013 at 01:01 PM.

  3. #3
    and the hat of copycat stevesmithx's Avatar
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    Quote Originally Posted by Hodor View Post
    My solution is still brute force and that makes me uneasy but I can't seem to get my lightbulb to light.
    There is a forum in Project Euler that opens up after you solve the problem. It has several interesting ways people used to solve the problem. For this particular problem, I could see many interesting solutions, some not using a computer at all.
    Hodor likes this.

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    Registered User whiteflags's Avatar
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    In other news, through some guesswork and playing around, I figured out Euler 5 on paper before I ever wrote an algorithm for it so now I would essentially have to work backwards.
    Granted, it is probably an easier problem than this one.
    I wonder if the site accepts functions that do no calculations at all.
    Hodor likes this.

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