1- 187 In a game, the "magician" asks a person to think of a three-digit number $(abc)$ (where $a, b, c$ are the decimal digits of the number in order), and asks this person to select 5 numbers $(acb), (bac), (bca), (cab)$, and $(cba)$, and to find the sum $N$ of these 5 numbers, and tell the sum $N$ to the "magician". Then, the "magician" can reveal the number $(abc)$ that the person thought of.

Now, let $N=3194$. Please act as the "magician" and find the number $(abc)$.

将上面的文本翻译成英文，请保留源文本的换行和格式，直接输出翻译结果。
[Solution] $(a b c)+N$
$$\begin{array}{l}
=(a b c)+(a c b)+(b a c)+(b c a)+(c a b)+(c b a) \\
=222(a+b+c) .
\end{array}$$

Therefore, we should find a multiple of 222, $222k$, such that it is greater than $N$ (since $(a b c) \neq 0$), and less than $N+1000$ (since $(a b c)$ is a three-digit number), and the sum of the digits of $222k-N$ is $k$. This way, $222k-N$ is the solution $(a b c)$.

Since $N=3194$, and
$$14 \times 222<3194<19 \times 222$$

Thus, $k$ could be $15, 16, 17, 18$.
Since $222 \times 15-3194=136$ and the sum of its digits is 10, which is not equal to 15,
$222 \times 16-3194=358$ and the sum of its digits is 16,
$222 \times 17-3194=580$ and the sum of its digits is 13, which is not equal to 17,
$222 \times 18-3194=802$ and the sum of its digits is 10, which is not equal to 18, thus $k=16$.
$$\begin{aligned}
\text { The required }(a b c) & =222 \times 16-3194 \\
& =358 .
\end{aligned}$$