In this weekâ€™s Sunday Puzzle, weâ€™re heading to the library. But not just any library.

### Sunday Puzzle #40: In Search of an Unusual Book

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?

Need a hint? Hereâ€™s a conceptually similar puzzle, the answer to which can help put you in the right frame of mind for tackling this problem:

Why must there certainly be at least two people in the world with exactly the same number of hairs on their head?

Weâ€™ll be back next week with the solutionsâ€”and a new puzzle! Got a great brainteaser, original or otherwise, that youâ€™d like to see featured? E-mail me with your recommendations. (Be sure to include â€śSunday Puzzleâ€ť in the subject line.)

### SOLUTIONS To Sunday Puzzles 37â€”39

Two weeks ago, I posed to you three straightforward puzzles that many people nevertheless answer incorrectly. All three were chosen from What is the Name of This Book?, an outstanding collection of math, logic, and paradoxical puzzles by Raymond M. Smullyan. The solutions appear below.

#### Solution to Sunday Puzzle #37: A Puzzling Proverb

The puzzle, restated:

An old proverb says: â€śA watched pot never boils.â€ť Anyone whoâ€™s bothered to test this proverb themselves knows the statement to be false; a pot placed on a hot stove will eventually boil, whether itâ€™s watched or not.

But what if we modify the proverb? What if, instead, it says: â€śA watched pot never boils unless you watch it.â€ť Stated more precisely, â€śA watched pot never boils unless it is watched.â€ť Is this statement true or false?

The statement is true. As Smulyan explains:

To say â€śP is false unless Qâ€ť is but another way of saying â€śIf P then Q.â€ť (For example, to say, â€śI wonâ€™t go to the movies unless you go with meâ€ť is equivalent to saying, â€śIf I go to

the movies, then you will go with me.â€ť) Thus the statement â€śA watched kettle never boils unless it is watchedâ€ť is but another way of saying, â€śIf a watched kettle boils, then it is watched,â€ť This, of course, is true, since a watched kettle is

certainly watched, whether it boils or not.

#### Solution to Sunday Puzzle #38: A Puzzling Picture (Part I)

Again, here is the puzzle restated:

A man was looking at a portrait when a passerby asked him, â€śWhose picture are you looking at?â€ť The man replied: â€śBrothers and sisters have I none, but this manâ€™s father is my fatherâ€™s son.â€ť

Whose picture was the man looking at?

The man is looking at a picture of his son. If you think that the man is looking at a picture of himself, donâ€™t worry, a lot of people do. If youâ€™re having trouble understanding the correct solution, try diagramming the relationships described in the problemâ€™s phrasing with pen and paper. Or, Smulyan suggests rephrasing the problem altogether:

(1) This manâ€™s father is my fatherâ€™s son

Substituting the word â€śmyselfâ€ť for the more cumbersome phrase â€śmy fatherâ€™s sonâ€ť we get

(2) This manâ€™s father is myself.

Now are you convinced?

#### Solution to Sunday Puzzle #39: A Puzzling Picture (Part II)

Once more, the puzzle is as follows:

Suppose, in the above situation, the man had instead answered: â€śBrothers and sisters have I none, but this manâ€™s son is my fatherâ€™s son.â€ť Now whose picture is the man looking at?