### Brain Teasers

# The Strange Library

In a certain library, no two books contain the same number of words, and the total number of books is greater than number of words in the largest book.

How many words does one of the books contain, and what is the book about?

How many words does one of the books contain, and what is the book about?

### Answer

One of the books is about nothing and has zero words.First, the library can be simplified into just two books. If there are two books, the greatest number of words possible is one and the other must have zero.

2 books: 1 word and 0 words.

Since the number of books is greater than the number of words in the largest book without repetition in number of words, the number of books will always be one more than the number of words in the largest book. There will always by necessity be books with every number of words possible less than the largest book, and there will always be a book with no words to increase the total number of books. This assumes (correctly) you can't have books with a negative number of words.

Following this logic, a library with three books has a book with two words, a book with one word, and a book with zero words.

3 books: 2 words, 1 word, and 0 words.

A library with n books has a book with n-1 words, a book with n-2 words, a book with n-3 words, and eventually a book with n-n words or zero words.

n books: n-1 words, n-2 words ... 0 words.

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## Comments

Excellent teaser. Well done.

Terrific! At first I thought there was not nearly enough information to reason out any kind of answer, but a bit of focus and thought made it clear. I actually took the base case lower than your two book library, asking what if there was only one book.

Simple and elegant problem statement with a fun and interesting answer. On my fave list!

Simple and elegant problem statement with a fun and interesting answer. On my fave list!

If it didn't have words or a subject, I didn't think it qualified as a book. But Staples sells completely blank books, so apparently I'm wrong. Well played!

It is not a library book w/o works. A ledger book or ?? BUT not A book. if if your setting were a table, shelf storehouse, rather than library. Bending reality is no no especially for LOGIC problem

prior comment " words " not works "

I only got this because I asked my grandson for help. He graduated college with a degree in math and finances. He had no trouble with it. He wasn't sure if a "journal" counted as a book in a library though, as stated above. Logically, if you were to go to a lending library, to borrow a book, what purpose would it serve to borrow a "journal"? In a reference library, there would be no purpose either. You are not allowed to deface library property. Of course, a Braingle library may have rules that defy all logic!

Yay! I'm excited to see this was chosen as a Daily Teaser! I still love this one.

To those nit picking the premise, the book with no words is a picture book. If the complaint is then that the pictures would be about something, then let it contain photographs from the U.S. television series, "Seinfeld", which was a show about nothing, making the book about nothing.

Hurray for creative new teasers making the ToD rotation!

To those nit picking the premise, the book with no words is a picture book. If the complaint is then that the pictures would be about something, then let it contain photographs from the U.S. television series, "Seinfeld", which was a show about nothing, making the book about nothing.

Hurray for creative new teasers making the ToD rotation!

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