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I was never really good at maths, trying to get back into it.

I have this question:

Pages 6 and 27 are on the same (double) sheet of a newspaper, what are the page numbers on opposite sides of the sheet and how many pages are there in the newspaper altogether

This seems like a trick question... I am not too sure how to take the logic, but I suppose pages 5 and 28 are the numbers on opposite sides of the page?

How do I get the total pages of the newspaper altogether? I am assuming we add the missing pages, 1 thru 4 (4 pages in total) to 27 to get 31?

Not sure how to solve this, and I have no answer key.

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It seems to me the main confusion with this question is how a newspaper's pages are arranged, which it does nothing to clarify. I.e., it's a bad question. –  Goos May 26 '13 at 5:57
    
Yeah... it's quite confusing... I typed it out verbatim. I am thinking they mean the broadsheet type of newspaper, and the numbers are on the same face of the paper and the opposites would be n-1 and n+1 respectively, but I am not too sure about the total number of pages, if it is merely adding pages 1-4 to 27 or if there's some other calculation involved –  Karuna-bdc May 26 '13 at 6:02
    
Your solution looks good except that, after determining that page 5 corresponds to page 28, you added the number of pages preceding page 5 (namely 4) to 27 rather than 28. –  Andreas Blass Mar 4 at 12:43
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2 Answers 2

up vote 2 down vote accepted

Assume the paper is formed by taking a pile of (printed) sheets of paper and folding it in half.

Look at the outside cover - this pairs up the first page and the last page on the outside. If there are $n$ pages altogether, the sum is $n+1$.

The other side of the same sheet has pages $2$ and $n-1$ - sum $n+1$.

In fact it is easy to see that the two pages on the same side of any of the original pieces of paper have numbers which add to $n+1$.

Here $n+1=33$ so $n=32$ - and the paper consists of $8$ folded sheets.

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Thanks for the explanation! I went out and bought a newspaper to wrap my head around it and when matched with your explanation it clicked in my head. Thanks again! –  Karuna-bdc May 26 '13 at 6:22
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pages 6 & 27 are mentioned in the question. its means there are $5$ pages on the left of page no. 6, obviously there will be also $5$ pages more on the right of $27$. so, $27 + 5 = 32$.

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