18. 9 judges score 12 athletes participating in a bodybuilding competition. Each judge gives 1 point to the athlete they consider to be in 1st place, 2 points to the athlete in 2nd place, $\cdots \cdots$, and 12 points to the athlete in 12th place. The final scoring shows: the difference between the highest and lowest scores of each athlete's 9 scores is no more than 3. Let the total scores of the athletes be $c_{1}$, $c_{2}, \cdots, c_{12}$, and $c_{1} \leqslant c_{2} \leqslant \cdots \leqslant c_{12}$. Find the maximum value of $c_{1}$.
18.9 judges cannot give 1 point to 5 or more athletes, because among 5 or more athletes, at least one athlete must be rated no less than 5 by a judge, while according to the problem, each of these 5 athletes is rated no more than 4 by each judge, which is a contradiction. Therefore, 9 judges can give 1 point to at most 4 athletes.
Below, we discuss different scenarios.
(1) If all judges give 1 point to a single athlete, then, $c_{1}=9$.
(2) If the 9 points of 1 given by 9 judges are concentrated on two athletes, then, one of these athletes must be rated 1 by at least 5 judges. Thus, by the problem's condition, the remaining judges give this athlete a score no greater than 4, so, $c_{1} \leqslant 5 \times 1+4 \times 4$ $=21$.
(3) If the 9 points of 1 given by 9 judges are concentrated on three athletes, then, the total score of these three athletes is no more than
$9 \times 1+9 \times 3+9 \times 4=72$.
Thus, $3 c_{1} \leqslant c_{1}+c_{2}+c_{3} \leqslant 72$.
Hence, $c_{1} \leqslant 24$.
(4) If the 9 points of 1 are distributed among 4 athletes, then, the total score of these 4 athletes is
$9 \times 1+9 \times 2+9 \times 3+9 \times 4=90$.
Thus, $4 c_{1} \leqslant 90$. Hence, $c_{1}<23$.
In summary, $c_{1} \leqslant 24$.
The scenario where $c_{1}=24$ is achievable, as shown in Table 2.
Table 2
\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|c|}
\hline & $A_{1}$ & $A_{2}$ & $A_{3}$ & $A_{4}$ & $A_{5}$ & $A_{6}$ & $A_{7}$ & $A_{8}$ & $A_{9}$ & $A_{10}$ & $A_{11}$ & $A_{12}$ \\
\hline$B_{1}$ & 1 & 4 & 3 & 2 & 5 & 6 & 7 & 9 & 10 & 8 & 11 & 12 \\
\hline$B_{2}$ & 1 & 4 & 3 & 2 & 5 & 6 & 7 & 9 & 10 & 8 & 11 & 12 \\
\hline$B_{3}$ & 1 & 4 & 3 & 2 & 5 & 6 & 7 & 9 & 10 & 8 & 11 & 12 \\
\hline$B_{4}$ & 4 & 3 & 1 & 5 & 2 & 7 & 9 & 6 & 8 & 11 & 10 & 12 \\
\hline$B_{5}$ & 4 & 3 & 1 & 5 & 2 & 7 & 9 & 6 & 8 & 11 & 10 & 12 \\
\hline$B_{6}$ & 4 & 3 & 1 & 5 & 2 & 7 & 9 & 6 & 8 & 11 & 10 & 12 \\
\hline$B_{7}$ & 3 & 1 & 4 & 2 & 5 & 9 & 6 & 7 & 11 & 10 & 8 & 12 \\
\hline$B_{8}$ & 3 & 1 & 4 & 5 & 2 & 9 & 6 & 7 & 11 & 10 & 8 & 12 \\
\hline$B_{9}$ & 3 & 1 & 4 & 2 & 5 & 9 & 6 & 7 & 11 & 10 & 8 & 12 \\
\hline Total & 24 & 24 & 24 & 30 & 33 & 66 & 66 & 66 & 87 & 87 & 87 & 108 \\
\hline
\end{tabular}