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Maths olympiad question · P2–P3★ Easy

Page numbers: olympiad question 1

An easy question on page numbers for P2–P3, 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 storybook's pages are numbered from 1 to 20.

How many digits are printed altogether?

Show the hints (2)
  1. Hint 1: Page 9 uses 1 digit. How many does page 10 use?
  2. Hint 2: Count the one-digit and two-digit page numbers separately.

Worked solution

Have a go first, then read the solution step by step.

  1. 1.Pages 1–9: 1 digit each, 9 in all.
  2. 2.Pages 10–20: 20 − 9 = 11 pages, 2 digits each, 22.
  3. 3.9 + 22 = 31.
  4. ⚠️Common mistake: answering 20, the number of pages, not of digits.

Answer: 31 digits

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