1999 AIME Problems/Problem 5

Problem

For any positive integer $\displaystyle x_{}$ , let $\displaystyle S(x)$ be the sum of the digits of $\displaystyle x_{}$ , and let $\displaystyle T(x)$ be $\displaystyle |S(x+2)-S(x)|.$ For example, $\displaystyle T(199)=|S(201)-S(199)|=|3-19|=16.$ How many values $\displaystyle T(x)$ do not exceed 1999?

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1999 AIME Problems/Problem 5

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