$$N$$ is a two$$-$$digit number. When $$N$$ is divided by $$9$$, the remainder is $$1$$. When $$N$$ is divided by $$10$$, the remainder is $$3$$. What is the remainder when $$N$$ is divided by $$11$$? ． 
Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems->Characteristics of Remainder 
The smallest possible $$N$$ is $$73$$, and $$73 \div 11\rm R7$$. 