## Library Puzzle

Here is a logic puzzle for kids:

— John has more than a thousand books, said Pete.
— No, he has less than one thousand books, said Ann.
— Surely, he has at least one book, said Mary.

If only one statement is true, are you sure you know how many books John has?

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1. #### nho:

YES!!!!!!!!!!!!!!!!!!!!!!!! John doesn’t have any books!!!!!!!!

More precisely, the intersection of the set comprised of the books John possesses with the set of all objects that can be called books is the empty set.

Proof: John has zero books. A set with zero elements (or, alternatively, with less than one element) must be isomorphic to some empty set. It is left to the reader to rigorously prove the intuitive assertion that all empty sets are in fact the same. QED.

I just realized i must be a mathematical prodigy. I think it’s due time for me to contribute to the advancement of mathematical knowledge. I hear that something called the ‘Riemann Hypothesis’ is still pending resolution. I’ll go check on it on Wikipedia and solve it in short order, so that i may thereafter dedicate myself to some REAL HARD problems…

2. #### nho:

Huh… It seems that the ‘Riemann Hypothesis’ is actually somewhat harder than i imagined.

And what the hell is a ‘prime’ number?

3. #### Tanya Khovanova:

Nho,

Your solution for the library puzzle is incomplete. Riemann Hypothesis will really have to wait.

4. #### Bill:

The answer is no. It seems that John must have either zero books or exactly one thousand.

The first statement cannot be true, because the third statement must then also be true, and we are told only one statement is true.

If the second statement is true, then the third statement must be false for the same reason. John has zero books.

If the third statement is true, the first and second statements must be false, and John has neither more nor less than one thousand books. John has one thousand books.

By the way, I’m really enjoying your blog! I found your site via the IBM Ponder This website, and I’ve been combing through your archives. I’m not a mathematician, which is why the first post I could really comment on was your puzzle “for kids.” You can imagine how well I do with the IBM puzzles…