Question 620548
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We need to find a 3 digit number ABC such that ABC times 101 is a five-digit palindrome.


In order for the product to be a palindrome given that one of the factors (101) is a palindrome, the other factor must be a palindrome also, hence we are actually looking for a three digit factor ABA.


*[tex \LARGE \, \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ABA]
*[tex \LARGE \, \ \ \ \ \ \ \ \ \ \ \ \ \ \ \times\ \underline{1\ 0\ 1}]
*[tex \LARGE \, \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ABA]
*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \ \ \underline{ABA\ \ }]


And the product will be a palindrome if and only if there is no carry when you add A + A.  Hence, the largest A can be is 4.  Find the largest 3 digit palindrome where the first and last digit is 4, then multiply that times 101 to find your largest 5 digit palindrome.


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it
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