A hard question on page numbers for P4–P5, 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 has 58 pages, numbered 1 to 58.
Each sheet has two pages: an odd page on the front and the next even page on the back (pages 1 and 2 share a sheet, for example).
One sheet has been torn out.
The remaining page numbers add up to 1688.
What is the higher page number on the torn-out sheet?
Show the hints (3)
💡Hint 1: If no sheet were missing, what would all the page numbers add up to?
💡Hint 2: The full total minus 1688 is the sum of the two torn-out pages.
💡Hint 3: The two torn pages add up to 23. They are consecutive: one odd, one even.
Worked solution
Have a go first, then read the solution step by step.
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