# Thread: A Chapter in A Novel

1. ## A Chapter in A Novel

As Bill had finished a chapter of the novel he was reading, his wife posed a curious question: "Dear, suppose you took the page numbers of the chapter you just read and added them together. What would you get?"

Bill summed them rather hastily in his head and replied, "Well, I may have to double-check my arithmetic. It's either 412 or 512, I'm not sure."

The wife instantly knew the correct answer, do you?

2. ## Re: A Chapter in A Novel

<span style="background-color: #FFFF00; color: #000000; font-weight: bold"><font color=yellow>Theoretically, both are possible: in a book consisting of 1,000 chapters of one page each, the "sum" of the pages of chapter 412 is equal to 412, and that of chapter 512 is equal to 512. But since Bill is not certain, this possibility can be excluded.

The answer is 412, for 512 = 2 to the power 8, a number with only even factors. The sum of at least two consecutive positive numbers can't have only even factors.</font color=yellow></span hi>

3. ## Re: A Chapter in A Novel

<center>
<hr>But since Bill is not certain, this possibility can be excluded.<hr>
.</center>
<span style="background-color: #FFFF00; color: #000000; font-weight: bold"><font color=yellow>I had not considered "one-page" chapters. Thanks for bailing me out! Your final conclusion is correct because as you illustrated: 512 is a power of 2 and no power of two can be expressed as the sum of consecutive integers.</font color=yellow></span hi>

4. ## Re: A Chapter in A Novel

Yeah, that's it! In fact, the wife's last name (before she married and became a Lancaster) was Dell.

5. ## Re: A Chapter in A Novel

The fact that his wife would instantly know probably also indicates she is a computer nerd, because she'd have known <span style="background-color: #FFFF00; color: #000000; font-weight: bold"><font color=yellow>512=2^8</font color=yellow></span hi> "instinctively".

Alan

Edited - well, a better computer nerd than me anyway, considering that <span style="background-color: #FFFF00; color: #000000; font-weight: bold"><font color=yellow>512 is in fact 2^9</font color=yellow></span hi> <img src=/S/grin.gif border=0 alt=grin width=15 height=15>

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