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 book's pages are numbered from 1 to 45.
A page number with two 3s counts twice.
How many times does the digit 3 appear in the page numbers?
Show the hints (2)
💡Hint 1: Count the two places separately: how many page numbers have 3 in the units? In the tens?
💡Hint 2: Page 33 has 3 in both places: count it once in each.
Worked solution
Have a go first, then read the solution step by step.
1.Units digit 3: 3, 13, 23, …, 43: 5.
2.Tens digit 3: 30 to 39: 10.
3.Page 33 has a 3 in each list, counted once in each. In all: 5 + 10 = 15.
⚠️Common mistake: counting page numbers instead of 3s, so page 33 counts once and you get 14.
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