2004 · Q114
114. A printer uses a total number of 4893 digits in order to number all the pages of his book. He starts with the digit 1 for the first page of the book. How many pages does the book have?
MathematicsNumber System
- A4892
- B2322
- C2100
- D1500
Explanation
Pages 1–9 use 9 digits, pages 10–99 use 90×2 = 180 digits, and pages 100–999 use 900×3 = 2700 digits — 2889 digits in all. The remaining 4893 − 2889 = 2004 digits number the four-digit pages: 2004/4 = 501 pages. Total pages = 999 + 501 = 1500.