From $$1$$ to $$9$$ there are~$1\times9=9$~digits.  From $$10$$ to $$99$$ there are~$2\times90=180$~digits.  From $$100$$ to $$110$$ there are~$3\times11=33$~digits.  In total, there are$9+180+33=222$~digits 
How many digits have to be written in order to write down every number from $$1$$ to $$110$$? 

1. $$110$$ 
2. $$109$$ 
3. $$221$$ 
4. $$222$$ 
5. $$330$$ 