22. Let $C$ be a circle with radius 2006 . Suppose $n$ points are placed inside the circle and the distance between any two points exceed 2006. What is the largest possible $n$ ?
22. Ans: 5.
Clearly, none of the points is in the centre $O$. Label the points $A_{1}, A_{2}, \ldots, A_{n}$ in clockwise direction. Note that no two points lie on the same radius. Now, for any two points $A_{i}, A_{i+1}$ $\left(A_{n+1}=A_{0}\right.$ ), the angle $\angle A_{i} O A_{i+1}>60$. Therefore, $n<6$. For $n=5$, just take the points to be the vertices of a suitable regular pentagon, then it will satisfy our condition. Therefore, $n=5$.