AMO · 2027 · Grades 6-7 · Self-study SET 28 Question 10

$\overline{XYX}$ and $\overline{YXY}$ are three-digit integers with distinct nonzero digits $X,Y$. How many different values can the sum $\overline{XYX}+\overline{YXY}$ have?

**Input:** Enter the integer only, without units.