To solve this problem, let's analyze the situation step by step.

1. Encyclopedia arrangement: The 23 volumes are placed in numerical order, with each volume being 3 inches thick. Each cover is 1/4 inch thick, meaning the pages between the covers are $3 - 2 \times (1/4) = 3 - 1/2 = 2.5$ inches thick.

2. Bookworm's path: The bookworm starts inside the front cover of the first volume and ends after eating through the back cover of the last volume. The important observation is that the bookworm does not eat through the entire thickness of each book because the covers' positioning matters:

   • The front cover of the first volume is on the right.
   • The back cover of the last volume is on the left.

Thus, the bookworm eats through the pages and covers in between, but skips the first volume's front cover and the last volume's back cover.

3. Books eaten:
   • The distance from the inside of the front cover of the first volume to the back cover of the 23rd volume is effectively the sum of the thicknesses of the 21 books in between volumes 2 and 22.
   • The total thickness of these 21 books is $21 \times 3 = 63$ inches.

Conclusion:

The bookworm eats through 63 inches of book.

Would you like to explore any details or have further questions?

Here are 5 related questions:

1. How would the solution change if the bookworm started outside the front cover of the first volume?
2. What if the covers were thicker, say 1 inch instead of 1/4 inch?
3. How would the result differ if the encyclopedia had 30 volumes?
4. If the worm ate diagonally through the books, how would you calculate its path?
5. Could you compute the total weight of the books given the thickness and an average page density?

Tip: When solving geometric problems like this, visualizing the setup often simplifies understanding key distances!