**The Bookworm And The Encyclopedias**

**- The Solution**

Last Monday I posed a simple math puzzle:

A set of 10 encyclopedias is sitting on a bookshelf in left-to-right numerical order.

Each single volume contains 1,000 pages.

A bookworm eats its way directly and linearly through them in a straight line.

It starts on page 1 of volume 1.

It ends on page 1,000 of volume 10.

Question: Not counting any covers, flysheets, etc., how many pages does the bookworm eat ?

The first step to the solution, which many of you realised, is to notice the way books are placed on a bookshelf. Page 1 of volume 1 is adjacent to page 1000 of volume 2. Page 1 of volume 9 is adjacent to page 1000 of volume 10. This means that we can discount volumes 1 and 10.

We only need to consider 8,000 pages. However, a book of 1000 pages is usually taken to be a book of 1,000

*numbered*pages. These are

*surfaces*. The bookworm bores through

*sheets of paper*.

The bookworm starts on surface 1 of volume 1 and ends on surface 1,000 of volume 10. Between those two surfaces it eats its way through 4,000 sheets of paper, i.e. 4,000 pages.

Kudos to tyro52 for noticing the ambiguity in my wording:

You asked how many pages the bookworm ate, and the answer to that is none, unless the bookworm was really, really big, or the encyclopedia was really, really small. (How's that for pedantry?) However, you clearly meant how many did it eat through ...Yes, I should have specified that the bookworm bores

*through*a page. :)

I posted this little puzzle to show how insidious the ambiguity in language can be.

Sometimes, pedantry can be a bonus when solving problems.

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