Question 46
In the plane there is a circle $\Gamma$ of radius $1$. At a point at a distance $2006$ from the center of $\Gamma$ is a cricket. This cricket wants to enter $\Gamma$ through jumps that satisfy the following condition: If $G$ and $G'$ are the positions of the cricket before and after a jump, then the bisector of segment $GG'$ has at least one point in common with $\Gamma$. Give the minimum number of jumps the cricket needs to achieve its goal, indicating how it does it. Show that with a number smaller than the one found, the cricket cannot reach $\Gamma$.