# Bookworm Riddle

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## Riddle

A $3$-volume set of books is on the shelf of a library, volumes $1$, $2$ and $3$ going as normal from left to right.

A bookworm starts eating from the front cover of volume $1$ and works its way through the the back cover of volume $3$.

Then it eats its way through all $3$ volumes, right?

## Solution

Wrong.

Just through volume $2$.

As can be seen, when the volumes are arranged on the shelf in the specified order:

- the front cover of volume $1$ abuts the back cover of volume $2$
- the front cover of volume $2$ abuts the back cover of volume $3$.

So the bookworm eats through volume $2$, from the back to the front.

## Sources

- 1944: Eugene P. Northrop:
*Riddles in Mathematics*... (previous) ... (next): Chapter One: What is a Paradox?