$4 \cdot 39$ Given 9 points in space, where no 4 points are coplanar. Find the smallest natural number $n$, such that when any $n$ line segments are drawn between the given points and each line segment is colored either red or blue, there will always exist a triangle with all sides of the same color.
[Solution] Label the 9 points as $A_{1}, A_{2}, \cdots, A_{9}$ and divide them into 5 groups: $\left\{A_{1}\right\},\left\{A_{2}, A_{3}\right\},\left\{A_{4}, A_{5}\right\}$, $\left\{A_{6}, A_{7}\right\}$, and $\left\{A_{8}, A_{9}\right\}$. If two points belong to adjacent groups (the 5th group and the 1st group are also considered adjacent), connect them with a blue line (represented by a solid line); if two points belong to non-adjacent groups, connect them with a red line (represented by a dashed line in the figure); if two points belong to the same group, do not connect them. In this case, the graph has a total of 32 lines, but there are no monochromatic triangles with all sides the same color, so the smallest natural number $n \geqslant 33$. On the other hand, when 33 lines are connected between these 9 points and each line is colored either red or blue, since the complete graph $K_{9}$ with 9 vertices has a total of 36 edges, it follows that the graph is missing 3 edges. Therefore, we can select 3 points from the 9 points such that each of the 3 missing edges has at least one endpoint among the selected 3 points. In this way, the subgraph with the remaining 6 points as vertices is a two-colored complete subgraph $K_{6}$. Thus, it must contain a monochromatic triangle.
In summary, the smallest natural number $n=33$.