The bookworm and the ten volumes

Question

Ten volumes of an encyclopaedia stand in order, volume 1 on the left, on a shelf, in the usual way with their spines facing out. Each volume has a block of pages 4 cm thick and two covers each 0.5 cm thick, so each volume is 5 cm wide.

A bookworm starts at page 1 of volume 1 and eats in a straight line through the books to the last page of volume 10.

How far does the worm travel? The obvious answer is 50 cm, or 49 after removing the outer covers. Both are wrong.

Accepted Answer

41 centimetres. Where page 1 is. Stand a book on a shelf with its spine towards you. Its front cover is on the right and its back cover on the left. Page 1 sits just inside the front cover, so it is at the right-hand edge of the volume. The last page sits just inside the back cover, at the left-hand edge. The worm's route. Starting at page 1 of volume 1 (the right edge of the leftmost book), the worm eats through: - the front cover of volume 1 (0.5 cm), - volumes 2 to 9 in their entirety (8 × 5 = 40 cm), - the back cover of volume 10 (0.5 cm), arriving at the last page of volume 10, which is …

The bookworm and the ten volumes

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