If only the positive integers from 1 through 49, inclusive, are written on a piece of paper, how many times is the digit 1 written?
We can start with cases
Case 1: How many of the one digit numbers have the digit 1? We easily know that there is only 1
Case 2: How many of the digit one is written from 10-19? We count that there are 10 digit ones in the first digit and one digit in the last digit. This gives us 11 digit 1 written.
Case 3: How many of the digit one is written from 20-49. There is only three which is 21, 31, and 41.
This gives us the total of 15 digit one written.
Hope this helped!