Three Digit Palindromes

What is the smallest three digit palindrome divisible by 18?  Can you solve this without a brute force examination of possibilities?

Communicated by Tom Chiari.

43 Comments

  1. Steven Miller on August 9, 2019 at 2:26 pm

    To: [email protected]
    To: [email protected]
    To: [email protected]
    To: [email protected]
    To: [email protected]
    To: [email protected]
    To A. N. Shanbhag
    several people have solved; I don’t post the answers (you are supposed to email me, but if you can’t you can post and I just don’t
    approve) as I don’t want to spoil people’s fun

    well done

    [[your email did not work]]



  2. Steven Miller on May 28, 2015 at 7:25 pm

    nice, but there is a solution when you interpret it the way most children would, namely divisible means it goes in a whole number of times and
    leaves a remainder of zero.



  3. Devon bibb on May 28, 2015 at 7:23 pm

    It’s 101 because it says divisible but not that it has to be an integer.



  4. Devon bibb on May 28, 2015 at 7:22 pm

    It’s 101 because it says divisible, but not that it has to be an integer
    PS I’m a child



  5. Steven Miller on August 1, 2014 at 2:18 am

    No, less.



  6. Dhaval Shah on June 23, 2014 at 6:33 pm

    414



  7. Steven Miller on December 8, 2012 at 9:04 pm

    anon — yes — [email protected]



  8. Steven Miller on November 7, 2012 at 8:27 pm

    yes (sjm1 AT williams.edu)



  9. Steven Miller on October 30, 2012 at 5:30 pm

    Rage: correct



  10. Steven Miller on October 16, 2012 at 2:22 am

    Thanks — normally the word divisible implies no remainder. /s



  11. Sebas on October 15, 2012 at 1:15 pm

    you might want to consider adding the demand that the outcome is a natural number as well… in it’s current form, the correct answer is 101 🙂

    (101 / 18 = 5 11/18 tadaa 😉 )



  12. Steven Miller on August 22, 2012 at 12:52 am

    Ravi: yes — please email at sjm1 AT williams.edu as I don’t like to post answers



  13. Steven Miller on August 13, 2012 at 1:47 am

    glad you’re enjoying it: sjm1 AT williams.edu



  14. miri on August 11, 2012 at 7:42 am

    coll tnx!



  15. Steven Miller on August 11, 2012 at 2:20 am

    I’m removing your post as you have the correct answer, but yes, please use in your math class and let me know how it goes (sjm1 AT williams.edu). I’m happy to have your students, if they do well, appear in the hall of fame.



  16. Steven Miller on July 23, 2012 at 1:04 am

    sent hint //s



  17. raian rahman on July 21, 2012 at 4:24 pm

    Can you please email the answer?i like to be ur fb frnd.pls give me ur fb id



  18. Steven Miller on July 20, 2012 at 5:37 am

    sure //s



  19. Liz on July 19, 2012 at 7:43 pm

    Can you please email the answer?



  20. Steven Miller on June 22, 2012 at 1:27 am

    it has to be an integer, yes. not sure what you mean by product; the number must be a palindrome and a multiple of 18.



  21. Joe on June 21, 2012 at 6:41 pm

    Does the three digit number’s product have to be 18 and a whole number?



  22. Steven Miller on May 1, 2012 at 2:48 pm

    something smaller works ..s



  23. shaheen on May 1, 2012 at 3:40 am

    414



  24. Steven Miller on April 17, 2012 at 2:03 pm

    not sure where you’re getting 333 from — that’s not the answer. //s



  25. Steve on April 17, 2012 at 4:19 am

    Still trying to figure out how 333 works … unless we’re using some unconventional definition of “divisible by” or “18” …



  26. Steven Miller on April 4, 2012 at 8:46 pm

    Ah, nice thinking! We want the smallest positive one…. :]



  27. Some guy on April 4, 2012 at 6:46 pm

    -828? Does that count as a palindrome?



  28. Steven Miller on March 29, 2012 at 8:17 pm

    xiaomilk: correct, not posting as it’s the soln



  29. Steven Miller on March 28, 2012 at 11:44 am

    nope — not three digits, and not divisible by 2.



  30. sauravshakya on March 28, 2012 at 10:31 am

    99



  31. Steven Miller on March 21, 2012 at 1:44 am

    Anonymous: correct!



  32. Anonymous on March 20, 2012 at 10:57 pm

    252



  33. Steven Miller on March 16, 2012 at 1:10 pm

    Unfortuantely not, as 108 isn’t a palindrome.



  34. noddy on March 16, 2012 at 12:34 pm

    is it 108?



  35. Steven Miller on March 12, 2012 at 8:34 pm

    people typically don’t consider that a 3 digit number, so look a bit higher (you’re on the right track)….



  36. Caitlin on March 12, 2012 at 8:12 pm

    Is the answer 090? If not, may I have the correct answer? thank you!



  37. Steven Miller on March 4, 2012 at 4:38 am

    no a smaller works. //s (email me at [email protected] for the soln)



  38. alaze on March 4, 2012 at 4:37 am

    so the awnser is 333????????



  39. Steven Miller on March 1, 2012 at 10:44 pm

    Rob: correct, well done! Not posting as it’s the soln.



  40. Steven Miller on February 11, 2012 at 3:37 am

    while 666 works, something smaller works as well…. //s



  41. Tim on February 11, 2012 at 3:10 am

    Is it 666?



  42. Steven Miller on February 9, 2012 at 5:29 am

    sure — shoot me an email at [email protected]



  43. Zach on February 9, 2012 at 4:32 am

    I know! May I “spill the beans” as it were?



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