A medium question on page numbers for P3–P4, with a step-by-step solution, diagrams and the answer. Common in the Hua Xia Cup's P2 to P5 papers: how many digits in all, how often a digit appears, and pages torn out.
The question
A dictionary's pages are numbered from 1 to 167.
How many digits are printed altogether?
Show the hints (2)
💡Hint 1: Page numbers have one, two or three digits. How many pages of each?
💡Hint 2: How many pages from 10 to 99? And from 100 on?
Worked solution
Have a go first, then read the solution step by step.
1.Pages 1–9: 9 pages × 1 = 9 digits.
2.Pages 10–99: 90 pages × 2 = 180.
3.Pages 100–167: 167 − 99 = 68 pages, × 3 = 204.
4.9 + 180 + 204 = 393.
⚠️Common mistake: thinking pages 10–99 are 89 pages.
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