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Sum of the page numbers (Posted on 2018-11-05) Difficulty: 1 of 5
What is the sum of the page numbers of the middle two pages
in a book with k pages?

See The Solution Submitted by Ady TZIDON    
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Solution Not so simple (spoiler) | Comment 1 of 3
The last page is k, the first is 1, so the average page is (k+1)/2.
If there are two middle pages, then their sum is k+1.

But there is only a clear set of middle pages if k is even. If k is odd, then the middle page is (k+1)/2.  The page before it is (k-1)/2 and the page after it is (k+3)/2.  Depending on which 2 you pick as the "middle" pages, their sum is either k or (k+2).

Final answer:  k+1 if k is even, 
                        k or k+2 if k is odd

And all of this assumes that we are using the word "page" consistently.  I choose not to say that a book with 50 sheets has page 49 and 50 on one of the middle sheets and 51 and 52 on the other, for a total of 202.

Edited on November 5, 2018, 10:06 am
  Posted by Steve Herman on 2018-11-05 09:35:58

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