HKIMO 2026 THPT (Grades 10–12 shared) National Final (Heat) Set 05 Question 23

Integers $x_1,\ldots,x_5$ satisfy $x_1\ge-3$, $x_2\ge-2$, $x_3\ge-1$, and $x_4,x_5\gt0$. How many solutions satisfy $x_1+\cdots+x_5=6$?