The roots of the following equations need to be found:

$$
\begin{gathered}
\log _{x-1} x-\log _{x-1} 6=2 \\
x^{4}-39 x^{3}+462 x^{2}-1576 x+1152=0
\end{gathered}
$$

The product of the two roots of the logarithmic equation and the roots of the algebraic equation indicate the positions of five letters in a word. How many times do the letters need to be permuted to obtain the name of a famous Hungarian general?
The roots of the first equation: $\frac{3}{2}$ and $\frac{2}{3}$; their product is 1. The roots of the second equation: 1, 4, 16, 18. The corresponding letters: á, á, d, p, r, which is a permutation of Árpád.

Number of solutions: 18.