For $$0.1\dot{1}99251\dot{7}$$ and $$0.2\dot{3}456\dot{7}$$, these two recurring decimals have the same $\text{n}^{}\text{th}$ decimal digit, that is $7$. What is the smallest value of $n$ that meets such requirement? 
Overseas Competition->Knowledge Point->Calculation Modules->Decimals->Recurring Decimals