In this week’s Sunday Puzzle, we’re heading to the library. But not just any 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?
Need a hint? Here’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?
We’ll be back next week with the solutions—and a new puzzle! Got a great brainteaser, original or otherwise, that you’d like to see featured? E-mail me with your recommendations. (Be sure to include “Sunday Puzzle” in the subject line.)
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.
The puzzle, restated:
An old proverb says: “A watched pot never boils.” Anyone who’s bothered to test this proverb themselves knows the statement to be false; a pot placed on a hot stove will eventually boil, whether it’s watched or not.
But what if we modify the proverb? What if, instead, it says: “A watched pot never boils unless you watch it.” Stated more precisely, “A watched pot never boils unless it is watched.” Is this statement true or false?
The statement is true. As Smulyan explains:
To say “P is false unless Q” is but another way of saying “If P then Q.” (For example, to say, “I won’t go to the movies unless you go with me” is equivalent to saying, “If I go to
the movies, then you will go with me.”) Thus the statement “A watched kettle never boils unless it is watched” is but another way of saying, “If a watched kettle boils, then it is watched,” This, of course, is true, since a watched kettle is
certainly watched, whether it boils or not.
Again, here is the puzzle restated:
A man was looking at a portrait when a passerby asked him, “Whose picture are you looking at?” The man replied: “Brothers and sisters have I none, but this man’s father is my father’s son.”
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, don’t worry, a lot of people do. If you’re having trouble understanding the correct solution, try diagramming the relationships described in the problem’s phrasing with pen and paper. Or, Smulyan suggests rephrasing the problem altogether:
(1) This man’s father is my father’s son
Substituting the word “myself” for the more cumbersome phrase “my father’s son” we get
(2) This man’s father is myself.
Now are you convinced?
Once more, the puzzle is as follows:
Suppose, in the above situation, the man had instead answered: “Brothers and sisters have I none, but this man’s son is my father’s son.” Now whose picture is the man looking at?
The man is looking at a picture of his father.