$17\div3=5R2$, so Matthias has $5$ groups of $3$ cuts, which means $5$ new heads grew. Thus, there are $17-5=12$ heads originally. 
To defeat a dragon, Matthias has to cut off all the dragon\textquotesingle s heads. If he can cut off $$3$$ of the dragon\textquotesingle s heads, one new head immediately grows. Matthias defeats the dragon by cutting off $$17$$ heads in total. How many heads did the dragon have at the beginning? 

1) $$8$$ 
2) $$9$$ 
3) $$10$$ 
4) $$11$$ 
5) $$12$$ 