The Bookworm's Journey
A ten-volume encyclopaedia stands on a shelf in the usual way: volume 1 on the left, volume 10 on the right, spines facing you, each book the right way up and the right way round.
Every volume is built the same: 3 cm of pages between two covers, and each cover is 2 mm thick.
A bookworm starts at page 1 of volume 1 and eats in a perfectly straight horizontal line until it reaches the last page of volume 10.
Volume 1 on the left. The red marks show where page 1 and the last page actually are once the books are shelved.
Answer to type: the distance the worm travels, in centimetres.
💡 I want a nudge
When a book stands on a shelf with its spine towards you, its first page is on the side nearest the *next* volume, not the previous one.
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Answer: 27.6
- Stand a book on a shelf, spine towards you. Its pages run from the front cover backwards — and the front cover of volume 1 faces volume 2, to the right. So page 1 of volume 1 is at the right-hand edge of volume 1, right up against volume 2.
- By the same reasoning, the last page of volume 10 is at its left-hand edge, right up against volume 9.
- So the worm never crosses the pages of volume 1 or volume 10 at all! It crosses only volume 1's front cover, then volumes 2 to 9 completely, then volume 10's back cover.
- Each whole volume is 3 cm + 2 × 0,2 cm = 3,4 cm. Volumes 2 to 9 is eight volumes: 8 × 3,4 = 27,2 cm.
- Add the two covers at the ends: 27,2 + 0,2 + 0,2 = 27,6 cm.
The trick: the arithmetic here is easy — the difficulty is entirely in noticing that the books are the wrong way round from what you imagined. Most people answer 34 cm (all ten volumes) and never doubt it. Before you calculate, draw the situation: half of all mistakes in word problems are made before the first multiplication.