# Her name is Cheryl.

I have an integer (in decimal representation) such that if I reverse its digits and add them up, I will get a new integer. I repeat this process until the resulting integer is a palindrome. We will denote an integer as a near-symmetric number if after twenty-five iterations, the resulting integer is still not a palindrome. What is the smallest positive near-symmetric number?

Details and assumptions

• A palindrome is a number that remains the same when its digits are reversed.

• As an explicit example, consider the integer to be $$49$$. The resulting number will be $$49 + 94 = 143$$. Repeat: $$143 + 341 = 484$$, which is a palindrome (after $$2 < 25$$ iterations). Thus $$49$$ is not a near-symmetric number.

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