# To be a bookworm

I have a complete set of encyclopaedias on my bookshelf, beautifully bound and neatly arranged with volume 1 on the left and volume 32 on the right. They were a talking point when I bought them 30-odd years ago and were regularly used, but as the internet took off so my use of them declined, preferring to use the online resources which were so conveniently at my fingertips.

So it was that the books remained unexamined for a number of years, until I recently moved house, whereupon I discovered an awful fact: an insect larva - specifically, a bookworm (Anobium punctatum, I've been told) - had found its way into the books and had munched its way through them.

The entomologist who identified it for me was curious about it, and took it for study. One question she did ask, though, was just how far the creature had travelled. I looked back at the books and, as I'd previously noted, confirmed that it had started at the first page of volume 1 (evidence suggests that it hatched there, the parent having departed a different way) and had travelled until it had reached the final page of the final volume, which is where I discovered it, so I gave this information to her, along with the measurements of the books, which were all identical:

• each cover is 6 mm thick
• each book is 40 mm thick in total

So, how far had the bookworm gone?

• So will you accept an answer? – Joe Z. Jul 7 '15 at 5:28

This riddle, like the question about the direction of a bus, is actually a trick riddle – the answer is very simple, but most people won't get it on the first try (and won't understand why their answer is incorrect until you tell them) due to an inadvertent oversimplification on their part. And just like the direction-of-the-bus riddle, this riddle depends on an implied convention.

The intended naïve line of thought is that for the bookworm to have travelled from the first page of volume 1 to the last page of volume 32, that it would have to have chewed clean through all 32 volumes of the encyclopedia, excepting the two covers on the edge of the row of the bookshelf. This gives us a total distance of $40 \times 32 - 6 \times 2 = 1268\ \text{mm}$.

However, this line of reasoning is incorrect, because the front cover of a book is on the right side of its spine. So the bookworm in fact didn't chew through the pages of volumes 1 or 32 at all – just their covers. This means that the actual distance travelled is $40 \times 30 + 6 \times 2 = 1212\ \text{mm}$.

However, even this answer is not necessarily correct. There's no information given about what language the encyclopedia is in. Certain languages like Chinese or Arabic are written from right-to-left, and the books in that language that are written in right-to-left generally have their front covers on the left side of the spine. Supposing the encyclopedia was written in one of these languages, the initial answer of $1268\ \text{mm}$ would in fact be correct.

Of course, this answer is slightly unsatisfactory because volumes of an encyclopedia written in a right-to-left language are generally also organized from right to left, so the fact that they were organized left-to-right on this particular shelf would seem somewhat unusual.

• +1. And for completeness, in the absence of any specific information to the contrary, the English-speaking conventions apply to the question which was written in English. – ClickRick Jul 2 '14 at 23:57
• I understand that. I'm just pointing out that it's a trick riddle because of that convention. – Joe Z. Jul 3 '14 at 0:20
• So if I were to make explicit that it is in English, which would lose nothing from the primary trick, would it become a better riddle? I'm open to suggestions which would turn it around from downvotes to upvotes. – ClickRick Jul 3 '14 at 7:15
• I'm pretty sure the English part isn't the problem (as you said, people will assume it's English if the problem is written in English) - it's more that people on this site don't really seem to like trick riddles much in the first place. – Joe Z. Jul 3 '14 at 14:26
• @ClickRick I don't really think this is a trick riddle with a stupid answer, everything is pretty clear in the question and undebatable solvable if the language formulation is added (I would just add it as flavour: A 32 volume british encyclopedia) – Falco Sep 29 '14 at 12:55

Is the answer 12 mm? He says nothing about having all the volumes, just that he arranged volume 1 and 32.

Building on the most upvoted answer, the first page of volume one sits on the right having only volume 1's cover separating it from volume 32 cover, that has its final page sitting on the left side of the book.

So the worm would travel the distance of two covers: $6 * 2 = 12$ mm.

• look up and learn some LaTeX, there you will learn how to use MathJax (to create nice formulas) – d'alar'cop Oct 14 '14 at 22:33

If the bookworm was born before the move and found while on the new home, the answer is obvious. It travelled the distance from the old home to the new home.

I feel like I'm missing something, but isn't this just $$(6*2)*32+(40-6*2)*32-6-6=1268 \text{ mm} = 1.268 \text{ m}$$ Which can be reduced to $$40*32-6-6 = 1268 \text{ mm}$$

The extra two $-6$ are for skipping the first cover of the first book (started on the first page) and the last cover of the last book (ended on the last page).

I don't see the puzzle here.

• Your answer is incorrect. To explain the correct answer would spoil the puzzle, however, because it depends on a specific trick. – Joe Z. Jul 2 '14 at 22:24
• @JoeZ. - I knew there had to be a trick that I was missing. I wasn't expecting that one, though. – Bobson Jul 2 '14 at 23:41