In writing the integers from 10 through 99 inclusive, how many times is the digit 6 written?
I want to count how many times 6 appears in the tens place and in the ones place. For the tens place, 6 appears 10 times, from 60 through 69. For the ones place, 6 appears 9 times, once in each of the following numbers: 16, 26, 36, ..., 96. So the total number of times 6 is written is 10 + 9 = 19. 