2. The final test. And Koshchei said to Ivan the Tsarevich: "You, Vanya, shall live until tomorrow morning. In the morning, you shall appear before me. I will think of three digits $a, b, c$, and you will tell me three numbers $x, y, z$. I will listen to you and tell you the value of the expression $a x + b y + c z$. Then guess what digits $a$, $b$, and $c$ I thought of. If you don't guess correctly - your head will be off..." Ivan the Tsarevich was saddened, went to think. He needs help. How?
2. We can choose $x=100, y=10, z=1$. Since $a, b, c$ are digits, the sum $S=a x+b y+c z=100 a+10 b+c=\overline{a b c}$, and Koschei the Deathless will name the required number himself.