Problem 15 · 2010 Math Kangaroo
Hard
Logic & Word Problems
work-backward
To make a newspaper with 60 pages, you need 15 sheets stacked inside one another. In one such newspaper, page 7 is missing. Which other pages are also missing from this newspaper?
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Answer: E — 8, 53 and 54
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Hint 1 of 2
One loose sheet has four pages on it: two near the front of the paper and two near the back.
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Hint 2 of 2
On any sheet the front page number and the back page number always add up to \(60 + 1 = 61\).
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Approach: the four pages on one sheet add to 61 in pairs
- On each sheet the page numbers pair up to total \(61\) (like \(1\) with \(60\), \(2\) with \(59\)).
- The front of the missing sheet holds pages 7 and 8, so the back holds \(61 - 7 = 54\) and \(61 - 8 = 53\).
- So pages 8, 53 and 54 are missing too — the answer is E.
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