Question 14
Natural numbers $a,b,c$ are described by three students. X says (1) $a^2+b^2+c^2=165$, (2) $bc=28$. Y says (1) $c>b$, (2) $b+c$ is divisible by 9. Z says (1) $c$ is divisible by 8, (2) $c=4$. Each student makes exactly one true and one false statement. Find $a+2b+3c$.
