3. Four equations with four unknowns. Find all solutions to the following system of equations:

$$
\left\{\begin{aligned}
x+y+z+w & =10 \\
x^{2}+y^{2}+z^{2}+w^{2} & =30 \\
x^{3}+y^{3}+z^{3}+w^{3} & =100 \\
x y z w & =24
\end{aligned}\right.
$$
3. By direct verification, we confirm that the set of numbers $(1,2,3,4)$ satisfies the first and fourth, as well as the second and third equations. Since all equations in the system are symmetric with respect to $x, y, z, w$, the other 23 permutations of the numbers $1,2,3,4$ are also solutions to the system. However, the product of the degrees of all four equations is 4!, so there are no other solutions to our system*.

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