How many copies of the digit 0 are there among the digits of the first 2016 positive integers?
"Positive integers" do not include the number 0. Keeping this in mind we get:
1 digit: 0
2 digit: 10, 20, 30, ..., 90 => 9
3 digit: _00, _01, _02, ..., _09, _10, _20, ..., _90 => 20*9 = 180
4 digit: (try to do this one by yourself)
Add the cases together to get the final answer.