What is the last digit of the smallest positive integer whose digits add to $$2022$$? ． 
Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems->Questions involving Divisions with Remainders
For the number to be as small as possible, we need the number of digits to be as small as possible.  For instance, $$111\cdots 1 (2022\textasciitilde1\text{s})$$ has a digit sum of $$2022$$, but it is a much larger number than $$333\cdots 3 (674\textasciitilde3\text{s})$$, which also has a digit sum of $$2022$$. Clearly, to reduce the number of digits in the number, we need to make as many as possible of the digits in the number equal to $$9$$.  Now $$2022 \div9 = 224$$ remainder $$6$$, so the smallest positive integer with digit sum of $$2022$$ is $$699\cdots 9 (224\textasciitilde9\text{s})$$. Its last digit is $$9$$. 