A book has its pages numbered 1 to 100. Counting every appearance separately, how many times is the digit 9 printed in those page numbers?

Count the two places a 9 can sit. As a units digit it appears on pages 9, 19, 29, 39, 49, 59, 69, 79, 89 and 99 — ten times. As a tens digit it appears on pages 90 to 99 — ten more. Page 100 has no 9 at all. The total is 10 + 10 = 20, and note that page 99 rightly contributes two of them. The traps: 19 is the number of pages that contain a 9 somewhere, which is not the same as the number of 9s printed, because page 99 carries two; 10 counts only the pages ending in 9; 11 counts the ten pages 90 to 99 and adds page 9.