$3+$ $[$ Convex Polygons $]$

In a convex 13-gon, all diagonals are drawn. They divide it into polygons. Among them, we take the polygon with the largest number of sides. What is the maximum number of sides it can have?
From each vertex of the original 13-gon, no more than two diagonals emerge, which are sides of the considered polygon. Each diagonal corresponds to two vertices, so the number of sides of the considered polygon does not exceed 13. An example of a regular 13-gon shows that the number of sides of the polygon obtained by cutting can be equal to 13.

## Answer

13.