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1999 AIME Question 5

AIME · 1999 AIME

Question 5

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