Question 5
In an archery competition, there are $30$ contestants. The target is divided into two zones. A hit in zone $1$ is awarded $10$ points while a hit in zone $2$ is awarded $5$ points. No point is awarded for a miss. Each contestant shoots $16$ arrows. At the end of the competition, statistics show that more than $50\%$ of the arrows hit zone $2$. The number of arrows that hit zone $1$ and the number that missed the target are equal. Prove that there are two contestants with the same score.