Three, (11 points) There are four numbers. Each time, select three of them, calculate their average, and then add the other number. Using this method, four calculations were made, resulting in the following four numbers: 86, 92, 100, 106. (1) Find the four numbers, (2) Find the average of these four numbers.
Three, let these four numbers be $a, b, c, d$. We can get
$$
\left\{\begin{array}{l}
\frac{a+b+c}{3}+d=86, \\
\frac{b+c+d}{3}+a=92, \\
\frac{c+d+a}{3}+b=100, \\
\frac{d+a+b}{3}+c=106 .
\end{array}\right.
$$

Solving it, we get $a=42, b=54, c=63, d=33$.
$$
\frac{1}{4}(a+b+c+d)=48 \text{. }
$$

Answer: These four numbers are $42,54,63,33$; the average is 48.