Koschei the Deathless thinks of three two-digit numbers: $a, b, c$. Ivan Tsarevich must name three numbers: $X, Y$, $Z$, after which Koschei tells him the sum $aX + bY + cZ$. Tsarevich must guess the numbers thought of, or else he will lose his head. What numbers should he guess to stay alive?
Ivan Tsarevich can name the numbers $X=1, Y=100, Z=10000$, then Koschei will tell Ivan Tsarevich a six-digit number, the first two digits of which are the number $c$, the next two digits are the number $b$ and the last two digits are the number $a$.