Raymond Smullyan.


The Riddle of Scheherazade.

Raymond Smullyan's puzzles

Raymond Merrill Smullyan (/ˈsmʌli.ən/; born May 25, 1919) is an American mathematician, concert pianist, logician, Taoist philosopher, and magician.
Born in Far Rockaway, New York, his first career was stage magic. He then earned a BSc from the University of Chicago in 1955 and his Ph.D. from Princeton University in 1959. He is one of many logicians to have studied under Alonzo Church. (Wikipedia)
Raymond Smullyan (born 1919) is an American mathematician, a logician and a magician
Why should I worry about dying? It's not going to happen in my lifetime!
I have free will, but not of my own choice. I have never freely chosen to have free will. I have to have free will, whether I like it or not!
If it is really true that you cannot resist them, then you are not sinning of your own free will and hence (at least according to me) not sinning at all.
There is nothing like a naturalistic orientation to dispel all these morbid thoughts of "sin" and "free will" and "moral responsibility."
Medical opinions differed as to the cause of this "humor" disease.
From what little was known about the subject, insincerity itself was regarded as another form of psychosis but one which was exceedingly rare.
Humor could not flourish in a wholly serious and rational atmosphere.
Metaphysical problems about "mind" versus "matter" arise only from epistemological confusions.
Of course the falsity of the fact that you believe it is red implies that you don't believe it is red. But this does not mean that you believe it is not red!
I believe that either Jupiter has life or it doesn't. But I neither believe that it does, nor do I believe that it doesn't.
en.wikiquote.org


Edward and Edwin (The twin puzzle).


There is a pair of identical twins named Edward and Edwin, who are indistinguishable in appearance.
One day shortly after they were grown, a strange disease struck them both and changed their lives forever.
Henceforth, each twin was in one of three psychological states — State 1, or State 2, or State 3 — that alternated in a constant cyclical pattern: 1, 2, 3, 1, 2, 3, 1,... and so on.
Curiously enough, at any given time, both brothers were in the same state — both were in either State 1, or State 2, or State 3.
There was, however, a crucial difference. Edward always lied when he was in State 1, but told the truth in the other two states.
Edwin, on the other hand, lied when in State 2, but told the truth when in State 1 or State 3.
One day, one of the brothers was asked: “Are you either Edwin in State 2 or Edward not in State 1?”

From his answer, is it possible to deduce what state he is in?
From his answer, can one deduce whether he is Edward or Edwin?


     

Answer: You cannot tell what state he is in, but you can tell who he is. Suppose he answers yes. If he is in a truthful state, then he really is either Edwin in State 2 or Edward not in State 1. But he then can't be Edwin in State 2 (in which he lies); hence he must be Edward, but not in State 1.
On the other hand, if he lied, then, contrary to what he said, he is neither Edwin in State 2 nor Edward not in State 1; hence he is either Edwin not in State 2 (and thus in a truthful state) or Edwin in State 1, but he can't be Edwin not in State 2, since he lied; hence he must be Edward in State 1.
This proves that if he answers yes, he must be Edward (maybe in State 1 or maybe not).
Now, suppose he answers no. If his answer is truthful, then he is neither Edwin in State 2 nor Edward not in State 1; hence he is either Edwin not in State 2 or Edward in State 1. But he can't be Edward in State 1, since he told the truth; so he must be Edwin (but not in State 2).
On the other hand, if he lied, then he is either Edwin in State 2 or Edward not in State 1, but the latter alternative is not possible (since Edward not in State 1 doesn't lie), so he must then be Edwin in State 2. Thus, if he answers no, he must be Edwin.
In summary, if he answers yes, he is Edward, and if he answers no, he is Edwin.


This is the puzzle in precise words from the source: www.olimu.com (inactive)

Knights and Knaves.


On a fictional island, all inhabitants are either knights, who always tell the truth, or knaves, who always lie.
John and Bill are residents of the island of knights and knaves.

Question 1
John says: We are both knaves
Who is what?

Question 2
John: If (and only if) Bill is a knave, then I am a knave.
Bill: We are of different kinds.
Who is who?

Question 3
John and Bill are standing at a fork in the road. You know that one of them is a knight and the other a knave, but you don't know which. You also know that one road leads to Death, and the other leads to Freedom. By asking one yes/no question, can you determine the road to Freedom?


     

Solution to Question 1

This is what John is saying in a more extended form: "John is a knave and Bill is a knave."
If John were a knight, he would not be able to say that he was a knave since he would be lying. Therefore the statement "John is a knave" must be true.
Since knaves lie, and one statement is true, the other statement must be false. Therefore the statement "Bill is a knave" must be false which leads to the conclusion that Bill is a knight.
The solution is that John is a knave and Bill is a knight.

Solution for Question 2

John is a knave and Bill is a knight.
In this scenario, John is saying the equivalent of "we are not of different kinds" (that is, either they are both knights, or they are both knaves).
Bill is contradicting him, saying "we are of different kinds".
Since they are making contradictory statements, one must be a knight and one must be a knave.
Since that is exactly what Bill said, Bill must be the knight, and John is the knave.

Solution to Question 3

There are several ways to find out which way leads to freedom.
One alternative is asking the following question: "Will the other man tell me that your path leads to freedom?"
If the man says "No", then the path does lead to freedom, if he says "Yes", then it does not.
The following logic is used to solve the problem.
If the question is asked of the knight and the knight's path leads to freedom, he will say "No", truthfully answering that the knave would lie and say "No".
If the knight's path does not lead to freedom he will say "Yes", since the knave would say that the path leads to freedom.
If the question is asked of the knave and the knave's path leads to freedom he will say "no" since the knight would say "yes" it does lead to freedom.
If the Knave's path does not lead to freedom he would say Yes since the Knight would tell you "No" it doesn't lead to freedom.
The reasoning behind this is that, whichever guardian the questioner asks, one would not know whether the guardian was telling the truth or not. Therefore one must create a situation where they receive both the truth and a lie applied one to the other. Therefore if they ask the Knight, they will receive the truth about a lie; if they ask the Knave then they will receive a lie about the truth.
Note that the above solution requires that each of them know that the other is a knight/knave.

An alternate solution is to ask of either man, "What would your answer be if I asked you if your path leads to freedom?"
If the man says "Yes", then the path leads to freedom, if he says "No", then it does not.
The reason is fairly easy to understand, and is as follows:
If you ask the knight if their path leads to freedom, they will answer truthfully, with "yes" if it does, and "no" if it does not. They will also answer this question truthfully, again stating correctly if the path led to freedom or not. If you ask the knave if their path leads to freedom, they will answer falsely about their answer, with "no" if it does, and "yes" if it does not.
However, when asked this question, they will lie about what their false answer would be, in a sense, lying about their lie. They would answer correctly, with their first lie canceling out the second. This question forces the knight to say a truth about a truth, and the knave to say a lie about a lie, resulting, in either case, with the truth.

Another alternative is to ask: "Is either one of the following statements correct?
You are a Knight and at the same time this is the path to freedom; or you are a knave and this is not the path to freedom".

More alternatives for a question to ask can be found using Boolean algebra.


 

The Politician Puzzle
Flickr.com/knonie



The Politician Puzzle.


A certain convention numbered 100 politicians. Each politician was either crooked or honest. We are given the following two facts:

• At least one of the politicians was honest.
• Given any two of the politicians, at least one of the two was crooked.


Can it be determined from these two facts how many of the politicians were honest and how many of them were crooked?


     

Answer: We are given the information that at least one person is honest.
Let us pick out any one honest person, whose name, say, is Frank. Now pick any of the remaining 99; call him John.
By the second given condition, at least one of the two men--Frank,John--is crooked. Since Frank is not crooked, it must be John.
Since John arbitrarily represents any of the remaining 99 men, then each of those 99 men must be crooked.
So the answer is that one is honest and 99 are crooked.

Another way of proving it is this:
The statement that given any two, at least one is crooked, says nothing more or less than that given any two politician, they can't be both honest; in other words, no two are honest.
This means that at most one is honest. Also (by the first condition), at least one is honest. Hence exactly one is honest. The Politician Puzzle
Image source: silentwhisperss.wordpress.com.--> New_year_resolutions


The Politician Puzzle
Flickr.com/knonie



The Politician Puzzle.


A certain convention numbered 100 politicians. Each politician was either crooked or honest. We are given the following two facts:

• At least one of the politicians was honest.
• Given any two of the politicians, at least one of the two was crooked.


Can it be determined from these two facts how many of the politicians were honest and how many of them were crooked?


     

Answer: We are given the information that at least one person is honest.
Let us pick out any one honest person, whose name, say, is Frank. Now pick any of the remaining 99; call him John.
By the second given condition, at least one of the two men--Frank,John--is crooked. Since Frank is not crooked, it must be John.
Since John arbitrarily represents any of the remaining 99 men, then each of those 99 men must be crooked.
So the answer is that one is honest and 99 are crooked.

Another way of proving it is this:
The statement that given any two, at least one is crooked, says nothing more or less than that given any two politician, they can't be both honest; in other words, no two are honest.
This means that at most one is honest. Also (by the first condition), at least one is honest. Hence exactly one is honest. The Politician Puzzle
Image source: silentwhisperss.wordpress.com.--> New_year_resolutions