Multiplying ones will always give you palindromic numbers.
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It only works up to 111,111,111, and you can see why if you do the multiplication longhand. When you get up to ten 1's, when you do the addition to get the final answer you'll have one column add up to ten, forcing you to perform regrouping and ruining the palindrome. 1,111,111,111 squared is 1,234,567,900,987,654,321
Like jqavins said, it will work farther if you use hexadecimal. 1,111,111,111 x 1,111,111,111 will get you 1,234,567,89A,987,654,321; 11,111,111,111 x 11,111,111,111 will get you 123,456,789,ABA,987,654,321, and so on.