$7 \cdot 32$ Find the smallest natural number $n$, such that every convex 100-gon can be represented as the intersection of $n$ triangles.
[Solution] From the vertices of a convex 100-gon, select 1 vertex every 1 vertex, totaling 50 vertices. Using each of these vertices as one vertex of a triangle, and the two adjacent sides of the convex 100-gon extending from this vertex as the two sides of the triangle, take 1 point on each of these two lines as the other two vertices of the triangle, such that the triangle contains the convex polygon within itself or on its boundary. Clearly, the convex 100-gon is precisely the intersection of these 50 triangles (see the left figure below).

On the other hand, when one side of the convex 100-gon is much longer and the other sides are very short, for example, taking an inscribed 100-gon in a segment of a circle, with the other 99 sides being equal, when representing it as the intersection of several triangles, any one triangle can intercept at most two of the short sides of the polygon. Therefore, at least 50 triangles are needed to intercept the convex 100-gon.
In summary, the smallest natural number $n=50$.