Given a segment $OA$. From the end of the segment $A$, 5 segments $A B_{1}, A B_{2}, A B_{3}, A B_{4}, A B_{5}$ emerge. From each point $B_{i}$, five new segments can emerge or no new segments at all, and so on. Can the number of free ends of the constructed segments be 1001? By a free end of a segment, we mean a point that belongs to only one segment (excluding point $O$).
When conducting five segments from the end of a segment, 5 new free ends appear and one old end disappears. As a result, the number of free ends increases by 4. Therefore, if the five segments are conducted $k$ times, the number of free ends is $4k + 1$. With $k=250$, we get the required number of free ends.

## Answer

It can be done.