Bookworms--The Solution

Recall Monday's brain teaser:

Imagine you have a twelve volume set of books sitting in order on the bookshelf. Each 400 page volume is exactly the same size: the covers are each .25" thick and 400 pages is .75" thick.

So if a bookworm begins eating on page one of volume one and, following a straight line, continues eating until she reaches the last page of the final volume, how far has she traveled?

Yesterday's discussion revealed several common wrong answers: viz., 15", 12" and 14.5" are all incorrect.

The real clue was in the discussion of blogs and document review.

The correct answer is 13".

To get the right answer you have to observe that when the books are properly shelved, each volume has page 400 on the left and page 1 on the right. Inspect a book placed vertically on a shelf and convince yourself this is true: the back cover is on the left, the front cover is to the right.

If the books were stacked on the floor with volume one on top and volume 12 on the bottom, then our bookworm would indeed proceed linearly from Volume 1, page 1 through Volume 12, page 400 and travel 14.5"

But notice when we shelve the books, we don't pick them up and shelve them with Volume 12 on the left; we rearrange them. Now the pages would go from 400 to 1, followed by 800 to 401, 1200 to 801, etc. (assuming for illustration purposes, they continued numbering the pages progressively from volume to volume).

So when our bookworm begins on page 1 of volume one and ends on page 400 of volume 12, she does not eat through the 400 pages of volumes one or twelve, saving herself two covers plus two sets of pages or 2 inches. So she only has to eat through the rest, a distance of 13 inches.

But you knew that already.

[Note: speaking of multiple volumes, J. K. Rowling recently announced the title of Book 6: "Harry Potter and the Half Blood Prince." And she revealed that the prince is neither Harry nor Voldemort.]