$$N$$ is a two$$-$$digit number. When $$N$$ is divided by $$5$$, the remainder is $$1$$. When $$N$$ is divided by $$11$$, the remainder is $$1$$. The smallest possible value of $N$ is~\uline{~~~~~~~~~~}~.(Adapted from $$2016$$ AMC $$8$$ Problem, Question \#$$5$$) 
Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems->Characteristics of Remainder 
Among $1, 56, 111$, \ldots~the smallest possible $$N$$ that satisfies the two conditions is $$56$$. 