The room numbers of a hotel are all three-digit numbers. The first digit represents the floor and the last two digits represent the room number. The hotel has rooms on five floors, numbered $$1$$ to $$5$$. It has $$35$$ rooms on each floor, numbered $$n01$$ to $$n35$$ where $$n$$ is the number of the floor. In numbering all the rooms, how many times will the digit $$2$$ be used? 
Overseas Competition->Knowledge Point->Counting Modules->Questions Involving Enumeration->Enumeration
Each floor has $$35$$ rooms. On every floor except floor $$2$$, the digit $$2$$ will be used for rooms \textquotesingle$$n02$$\textquotesingle, \textquotesingle$$n12$$\textquotesingle, \textquotesingle$$n20$$\textquotesingle{} to \textquotesingle$$n29$$\textquotesingle{} (including \textquotesingle$$n22$$\textquotesingle) and \textquotesingle$$n32$$\textquotesingle. Hence the digit $$2$$ will be used $$14$$ times on each floor except floor $$2$$. On floor $$2$$, the digit $$2$$ will be used an extra $$35$$ times as the first digit of the room number. Therefore the total number of times the digit $$2$$ will be used is $$5\times14+35 = 105$$. 