1. After 20 figure skaters have performed, 9 judges respectively assign them rankings from 1 to 20. It is known that the difference between any rankings given to each athlete does not exceed 3. If the sum of the rankings received by each athlete is arranged in an increasing sequence, $c_{1} \leqslant c_{2} \leqslant$ $\cdots \leqslant c_{20}$, find the maximum value of $c_{1}$.
(Tip: Let the set of athletes who have won first place be $A$. If $|A|=1$, then $c_{1}=9$; If $|A|=2$, then one of them wins no less than 5 first places, by the problem's condition we know $c_{1} \leqslant 5 \times 1+4 \times 4=21$; If $|A|=3$, similarly, we have $c_{1}+c_{2}+c_{3} \leqslant 1 \times 9+3 \times 9+4 \times 9=$ 72, so $c_{1} \leqslant 24$; If $|A|=4$, we have $c_{1}+c_{2}+c_{3}+c_{4} \leqslant 1 \times 9$ $+2 \times 9+3 \times 9+4 \times 9=90$, so $c_{1} \leqslant 22 ;|A| \geqslant 5$ is impossible. Therefore, $c_{1} \leqslant 24$.)