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A-palindrome-is-a-number-that-remains-the-same-when-its-numbers-are-reversed-The-number-n-and-n-192-are-three-digit-and-four-digit-palindromes-respectively-What-is-the-sum-of-the-digits-of-m-Can-




Question Number 110587 by Aina Samuel Temidayo last updated on 29/Aug/20
A palindrome is a number that  remains the same when its numbers  are reversed. The number n and  n+192 are three−digit and  four−digit palindromes respectively.  What is the sum of the digits of m?     Can this be solved mathematically?
Apalindromeisanumberthatremainsthesamewhenitsnumbersarereversed.Thenumbernandn+192arethreedigitandfourdigitpalindromesrespectively.Whatisthesumofthedigitsofm?Canthisbesolvedmathematically?
Answered by floor(10²Eta[1]) last updated on 29/Aug/20
we just need to get a 4 digit palindrome  that when subtracted by 192 we get a   palindrome with 3 digits  the first 4 digits palindromes are:  1001  1111  1221  ....  notice that we can stop here because if we   subtract 192 of 1221 we dont get a   3 digit number.  now we just need to test those 2 cases:  1001−192=809. not a palindrome.  1111−192=919. is a palindrome  so n=919 and the sum of the digits  is 9+1+9=19
wejustneedtogeta4digitpalindromethatwhensubtractedby192wegetapalindromewith3digitsthefirst4digitspalindromesare:100111111221.noticethatwecanstopherebecauseifwesubtract192of1221wedontgeta3digitnumber.nowwejustneedtotestthose2cases:1001192=809.notapalindrome.1111192=919.isapalindromeson=919andthesumofthedigitsis9+1+9=19
Commented by Aina Samuel Temidayo last updated on 29/Aug/20
Thanks.
Thanks.

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