22 Find all positive integer tuples $(x, y, z, w)$, such that $x!+y!+z!=w!$.

Translate the above text into English, please retain the original text's line breaks and format, and output the translation result directly.
$$
\begin{array}{l}
22. \text{Let } x \leqslant y \leqslant z, \text{ and } w! = z! + y! + x! \\
z \leqslant 2
\end{array}
$$

If $z=1$, then $x=y=z=1$, at this time $w!=3$, there is no such $w$, so $z=2$. At this time $w \geqslant 3$, hence
$$w!\equiv 0(\bmod 3)$$

Therefore,
$$x!+y!\equiv 1(\bmod 3)$$

And
thus it can only be
$$\begin{array}{l}
x \leqslant y \leqslant 2 \\
x=y=2
\end{array}$$

At this time
hence
$$(x, y, z, w)=(2,2,2,3)$$