> I suppose the question doesn’t mention that volume 1 is on the left and volume 2 is on the right but I guess that would be assumed by any speakers of left to right languages.

The answer is supposed to be 4mm; the only way for that to work if volume 1 is on the left is for the bookworm to gnaw its way out of the book from v.1.p.1, cross the outside of the two books without gnawing anything until it reaches the back cover of volume 2, and then gnaw its way through that cover to reach the final page of volume 2.

I don't think that's what the question has in mind. The point of being a bookworm is that you don't leave the book. So the answer would appear to require that volume 2 is shelved in front of volume 1. I don't know why that would be the case.

Diagram for the desired solution, on the shelf:

  V1 V2

In that order you can see that the pages in each book are in this order:

  |    V1    |    V2    |
  +----------+----------+
  |9876543210|9876543210|

(0-indexing of the pages for fun, plus it fit better, also reminded me of annoying protocol specs that mix 0- and 1-based indices with different elements)

The first page of V1 is the rightmost page (shelved) of Volume 1, and the last page of V2 is the leftmost page (shelved) of Volume 2. So the bookworm ends up going only through the covers. Having volumes shelved in order from left-to-right is conventional in left-to-right languages since that's the same direction we read, and you'd want to "read" through the titles to find the volume you wanted.

This is incorrect. You seem to be making the same error as the author says the editors made in the footnote at the bottom.

If volume 1 is on the left, and the worm goes from page 1 of volume 1 to the last page of volume 2, it travels 4mm in a straight line.

Page 1 of volume 1 and the last page of volume 2 will be right next to each other, if volume 1 is on the left.

Wow, this relies on both books being in the same orientation, with front cover to the right. It assumes a lot. For perspective, I for years kept books shelved upside down because that orientation was easier for me when reading spines.

I guess it relies on the books being ordered and arranged the same way they'd be in every single bookstore and library in the world (in left-to-right ordering countries).

But it's true, maybe this is too much to assume. Most of the time when I've seen this puzzle it's shown the book spines in an image to make it clear, and many people still can't get it. Then again, that would rely on knowing whether it was using top-to-bottom or bottom-to-top book title orientation, so perhaps the only solution is for the author to spell out "the first page of volume 1 is next to the last page of volume 2."

> in every single bookstore and library in the world

Not so fast. Some cultures (Japan for one, I think China and Taiwan as well?) have page-ordering right-to-left but books are generally stacked left-to-right from what I've seen (and in ether case bookstores don't order volumes differently depending on if it's native right-to-left books or foreign right-to-left ones).

German books have the orientation of the writing on the spine flipped. I don't like storing books upside down, so it makes a mess in my mixed English and German bookshelf.

There's a language-wide order in Germany of direction the of writing on the spines of a books?

I just checked my bookshelf and my books go both ways.

Ah. I just checked, and while all the English ones seem to have a consistent orientation, the German ones indeed don't. Never noticed, huh...

The point with this question is that if volume 1 is on the left and volume 2 is on the right, the first page of volume 1 is facing right and the last page of volume 2 is facing left, so the only thing between them is the two covers. Hence, the answer is 4 mm.

It also assumes that the pages aren't facing out.

could also be the case that the two volumes are empty, ie have no pages

The problem statement gives us that there are 2cm of pages in each book. So they are not empty. The confusion is in which order the books would be on the shelf, and consequently which direction the bookworm would be moving and through what.

what book has no pages? Also the problems states:

> The pages of each volume are 2 cm thick

The pages would be less than 20mm thick in that case.