Conference rusure::math

>1) sensus taker knocked at first house and asked " I need information about
>you and your wife. which, if either, is a knight a knight and which if either
>is a Knave?"
>husband answers: "we are both knaves"
>what type is the husband and what type is wife?

If the husband is a knight and tells the truth then this contradicts his
statement so the husband is a knave. If the wife is also a knave then the
husband's statement is true but this contradicts the fact that knaves always
lie so the wife must be a knight.

Result: The husband is a knave and the wife a knight.



>2)next house, sensus taker asked husband :" are both of you Knaves?"
>the husband replies "at least one of us is"
>what type is the husband and what type is wife?

If the husband is a knave then his statement is true and knaves always lie
so he must be a knight. In this case he tells the truth. As one of them is a
knave and he is a knight, his wife must be a knave.

Result: The husband is a knight and the wife a knave.



>3)next house, sensus taker asked the husband to say something about
>himself and his wife, all the husband said was "if I am a Knight, then
>so is my wife"
>what type is the husband and what type is wife?

Suppose the husband is a knave. In this case his statement should be false. The
only way for an implication to be false is that the antecedent is true (and the
consequent false). Thus the husband is a knight. This is a contradiction so the
husband can't be a knave. So the husband is a knight and his statement is true
and thus his wife is also a knight.

Result: Both are knights.



>4)next house, sensus taker interview couple, husband said:" my wife and
>I are of the same type"
>what type is the husband and what type is wife?

Puzzled?



I think you could phrase these questions in non-sexist language if you will
accept answers in terms of speakers and spouses, knights and knaves.



>5) Could any inhabitant in the island say
>   "if I am a knight then Santa Claus exists", if yes why, if no why?

Assuming Santa Claus does not exist then the answer is no.

As per 3) a knave can't make the statement because the only way to lie would
then be for the knave to be a knight (if you see what I mean). On the other
hand, if a truth-telling knight made the statement then this would imply the
existence of Santa Claus which by assumption I have ruled out. [I don't want
to disillusion our younger readers though.]



>this next one has a long answers and different ones:
>
>on Monday morning, professor said to class, "I will give you a surprise
>exam someday this week, on the morning of the day of the exam you will
>not know that this is the day of the exam"

I think this is discussed elsewhere as the prisoner's execution paradox.

        re .1
        
>>  >4)next house, sensus taker interview couple, husband said:" my wife and
>>  >I are of the same type"
>>  >what type is the husband and what type is wife?
>>
>>  Puzzled?
        
        A little.  Why didn't you answer #4?  :-)
        
        This could have two cases.  If the husband is a knave,
        then he is lying so his wife is a knight.  If the husband
        is a knight, then he is telling the truth so his wife is
        a knight.  So the result is that the wife is a knight,
        but we have no information as to the husband's type.
        
        Dan
        

>>on Monday morning, professor said to class, "I will give you a surprise
>>exam someday this week, on the morning of the day of the exam you will
>>not know that this is the day of the exam"
>
>I think this is discussed elsewhere as the prisoner's execution paradox.
    
    Note 805.  I'm still not sure I understand the explanation, but then I
    never was good at philosophy.
    
      John

    ref .1
>I think you could phrase these questions in non-sexist language if you will
>accept answers in terms of speakers and spouses, knights and knaves.
    please dont shoot the messagner, i was typing in what the author wrote.
    by the way, iam puzzled here, what sexist about the word husband and
    wife? i think we are going too far with this.
    
    (who would thought this topic will be argued in a math confrence ?)
    /naser
    

re .4
    
>    please dont shoot the messagner, i was typing in what the author wrote.
    
    OK, I accept that.
    
>    by the way, iam puzzled here, what sexist about the word husband and
>    wife? i think we are going too far with this.
>    
>    (who would thought this topic will be argued in a math confrence ?)
    
    I'll resist the temptation to rathole.
    
    By the way, does the book have anything to say about question 4? I
    concluded that there was insufficient information to answer the
    question (in particular to identify the type of the husband) and a
    previous reply agreed with me. This seems an unlikely situation.

    the author has an answer to number 4, if i remeber he said you could
    not find what the husband is, but you could deduce what the wife
    (soory the spouse) is, i'll write the excact answer tonite when i 
    get home.
    /naser
    

    solutions as per author:
    
    1) husband is Knave, wife is Knight
    2) husband is Knight, wife is Knave
    3) husband and wife are Knights
    4) wife must be Knight.
       reason: the husband is either a Knight or Knave, if he is a Knight,
       his statment is true, hence he and his wife really are of same type,
       which means his wife is also a knight.
       on the other hand, if he is a Knave, then his statment is false,
       hence he and his wife are of different types, which means that his
       wife must be a Knight.
    5) this has long answer and since it was covered befor i'll skip.
    the book has lots more intersting "Godel" type puzzles. it is a good
    book for those who like convoluted logic. cost ($17) by alfred a. knoff
    publishers.
    /naser
    

    Opps , i meant 5) in .7 relating to the "exam puzzle" not the santa
    clause puzzle. 5) was answered correct earlier.
    

    Tom, Dick, Harry are three brothers,
    Hearty, hale and youthful,
    And each of them is always lying,
    Or - is always truthful.
    
    "Most of them are truthful, though",
    Claimed their doting mother.
    So I went to ask the lads
    To tell about each other.
    
    Then Tom declared that Dick denied
    That Harry always lied.
    "Tom tells a lie, I tell you so",
    Brother Harry cried.
    
    I am confused, I must confess,
    And now I turn to you.
    Can you tell me who was lying
    And who is always true?
    
    
    (due to Marta Sved, University of Adelaide)

More information needed:


o	Which trait was inherited from the "doting mother" ?

o	Who wrote the poem ?

re .10
    
>o	Which trait was inherited from the "doting mother" ?
    
    Good question. I guess you are supposed to assume that the mother's
    statement is true.

>o	Who wrote the poem ?
    
    The author is attributed in .-2. I think you are supposed to assume
    that she is making only true statements.

>    "Most of them are truthful, though",
>    Claimed their doting mother.
        
        So at least two of them always tell the truth, and
        at most one of them always lies.
        
>    Then Tom declared that Dick denied
>    That Harry always lied.
>    "Tom tells a lie, I tell you so",
>    Brother Harry cried.
        
	It could be that Dick made no such denial, so that Tom
        is lying and Harry is telling the truth.  So one possible
        solution is that Tom always lies and Dick and Harry always
        tell the truth.
        
        On the other hand, if Tom was telling the truth, then Harry
        lied, and so Harry always lies, and thus Dick's denial was
        also a lie.  But that is too many liars; so the above (i.e.,
        Tom always lies and Dick and Harry always tell the truth)
        must be the only solution.
            
	Dan