Question 143
Sara is looking for a three-digit positive integer $\overline{xyz}$ ($z$ are ones, $y$ are tens, and $x$ are hundreds) which satisfies $1 \le x \lt y \lt z$ and the property that the sum of the numbers $\overline{xyz}$, $\overline{yzx}$, and $\overline{zxy}$ is a three-digit number which has equal digits. At most how many such three-digit numbers can Sara find?
(A) 3 (B) 5 (C) 7 (D) 9 (E) 11
(A) 3 (B) 5 (C) 7 (D) 9 (E) 11