20. The surname of a Russian writer consists of six letters. It is known that the numbers indicating the positions of these letters in the Russian alphabet are in the following ratios: the first is equal to the third; the second is equal to the fourth; the fifth is 9 more than the first; the sixth is 2 less than the sum of the second and fourth; if we triple the first, we get a number 4 less than the second; the sum of all these numbers is 83. Find the surname of the writer.
20. Let the first number be $x$, then the second is $(3 x+4)$, the third is $x$, the fourth is $(3 x+4)$, the fifth is $(x+9)$, and the sixth is $(6 x+6)$. According to the condition

$$
x+(3 x+4)+x+(3 x+4)+(x+9)+(6 x+6)=83
$$

from which $x=4$. The fourth letter of the alphabet is $\Gamma ;(3 x+4=16)$ the sixteenth letter is O; $(x+9=13)$ the thirteenth letter is L; $(6 x+6=30)$ the thirtieth letter is the soft sign. As a result, we get GOGOL.