(no subject)

[drewbear]

I recently started re-reading a favorite book called What Is the Name of This Book - The Riddle of Dracula and Other Logical Puzzles by Raymond Smullyan. Mr. Smullyan is/was (I think he's dead, but I'm not sure) a professor of mathematical logic. In this and his other books he smoothly leads the reader through the tenets of logic, starting with the most basic concepts and working all the way up to and through meta-logic and topics such as Gödel's Incompleteness Theorem. What's interesting is that he does so in an interesting and entertaining way. As an example, the following are some of the puzzles (and their answers behind the cut-tag) from the 2nd chapter.

1. A man was looking at a portrait. Someone asked him, "Whose picture are you looking at?" He replied: "Brothers and sisters have I none, but this man's father is my father's son." ("This man's father" means, of course, the father of the man in the picture.) Whose picture was he looking at?
   
2. A man is 100 yards due south of a bear. He walks 100 yards due east, then faces due north, fires his gun due north, and hits the bear. What color was the bear?
   
3. If an airplane crashes right on the border of the United States and Canada, in which country would you bury the survivors?

Try and get the answers before looking behind the tag.

1. The man is looking at a picture of his son. If you are skeptical, here is the logic: The first part of his statement ("Brothers...") tells us that he is an only child. The last part of his statement ("my father's son") tells us that he is referring to himself at that point. So we can therefore condense the statement to "This man's father is myself," which obviously means the picture is of his son.
   
2. The bear must be white, for it is a polar bear. The usual reasoning is that the bear is standing on the North Pole. Therefore, all points are south of it, and the hunter, by moving east, is not changing his relative distance from the bear at all. However, this is not the only proposed solution. It is possible that the hunter originates at a point so close to the South Pole that he completes at least one full circle in his eastward journey, thereby finishing at his original position. In my mind however, since polar bears don't (naturally) exist at the south pole, we must assume the solution of the north pole.
   
3. Neither! One would hardly wish to bury the survivors!
   

So how'd you do? And would anyone like me to post more logic puzzles from the book?