1. (1) Determine the range of values for the following sum: $S=\frac{a}{a+b+d}+\frac{b}{a+b+c}+\frac{c}{b+c+d}+$ $\frac{d}{a+c+d}$, where $a, b, c, d$ are any positive real numbers. (16th IMO Problem)
$$\begin{array}{l}
\text { 1. (1) Since } \frac{a}{a+b+d}+\frac{b}{a+b+c}\frac{a}{a+b+c+d}+\frac{b}{a+b}-\frac{b}{b+c+d}+\frac{c}{a+b+c+d}+\frac{d}{a+b+c+d}=1 \\
\text { Let } a \rightarrow+\infty, b=d=\sqrt{a}, c=1 \text {, the sum } \rightarrow 1, a=c \rightarrow+\infty, b=d=1 \text {, the sum } \rightarrow 2,
\end{array}$$
Therefore, the range of values for $S$ is the open interval $(1,2)$.