Among $64, 154$\ldots~the smallest possible $$N$$ that satisfies the two conditions is $$64$$, and $$64 \div 11\rm R9$$. 
$$N$$ is a two$$-$$digit number. When $$N$$ is divided by $$9$$, the remainder is $$1$$. When $$N$$ is divided by $$10$$, the remainder is $$4$$. What is the remainder when $$N$$ is divided by $$11$$? (Adapted from $$2016$$ AMC $$8$$ Problem, Question \#$$5$$) 
1) $$1$$ 
2) $$3$$ 
3) $$5$$ 
4) $$7$$ 
5) $$9$$ 