136. Twenty-four. In one book it was written: “Write the number 24 using three identical digits, different from 8. (There are two solutions to this problem.)”

The book also provided two answers: $22+2=24$ and $3^{3}-3=24$. Readers familiar with the old puzzle “Four Fours” and similar puzzles might ask why there are only the two solutions given above. Can you find more?
136. It is not difficult to represent the number 24 using three fours, fives, eights, or nines:

\[
\begin{gathered}
(4+4-4)! \\
\left(5-\frac{5}{5}\right)! \\
\left(\sqrt{9}+\frac{9}{9}\right)!
\end{gathered}
\]

The number 24 can also be represented using three ones, sixes, and sevens. Indeed,

\[
\begin{gathered}
\left(\frac{6}{.6}-6\right)!=24 \\
\left(7-\left[\sqrt{\frac{7}{.7}}\right]\right)!=24 \\
\left(1-\left[\sqrt{\frac{1}{.1}}\right]\right)!=24^{*}
\end{gathered}
\]