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 Very Difficult Logic Problems Sultan and his princess Goto page 1, 2  Next
 Sat Nov 22, 2008 4:15 pm  by ohsarcasm A wily young man wishes to marry the princess Arlena. Unfortunately, her father, the Sultan, is opposed to the marriage and is willing to buy the young man off. The Sultan, therefore makes the young man the following offer--"You get to make one statement. If the statement is false, you will be put to death and receive none of the following three things. If the statement is true, you may have one of the following three things, but I get to choose! The three things are: (1) Arlena's hand in marriage; (2) A cup filled with extremely valuable diamonds; (3) A magic lamp with a genie (who, unfortunately, cannot do marriages)." The wily young man, however, is too wily for his future father-in-law. He makes a statement such that the only way the Sultan can keep his promise is by giving the young man Arlena's hand in marriage. What was the statement?
 Thu Nov 27, 2008 8:38 am  by rj82330 Good one, this - only heard it will TWO options in the past. He says: "You will [i]not[/i] give me the diamonds or the genie".
 Mon Dec 22, 2008 10:08 pm  by alexonfyre If that were correct RJ couldn't the Sultan just say "False, I chose the diamonds for you." and death. I think the actual answer is: "If you do not let me marry your daughter, I will be put to death" Meaning that if the king chooses diamond or genie and lets him live, he will be telling a lie and the king will have to put him to death, which would in turn create a paradox as he would be telling the truth at that point. The only resolution to the paradox is to allow the prince to marry his daughter. If the Sultan chooses to put him to death later, that would be another story, but in the mean time the Sultan would have to give up his daughter's hand in marriage.
 Tue Dec 23, 2008 11:39 am  by rj82330 My thinking was that with the three variable given, there is only one way to prevent creating either a paradox, or a contradiction in the question. I had the young man say "you [i]will not[/i] give me certain presents" not "you [i]would not have[/i] given me certain presents". (You have the sultan saying "I [i]chose[/i]"). In this case, if the sultan wants to say "False, I will give you the diamonds", he has to actually fork over a present to prove the young man's statement false: but the scenario above doesn't allow for the young man to be given a present in the event of his making a false statement and ultimately being executed. - Contradiction If the sultan acknowledges that the young man's statement is true - because he is going to be executed rather than receiving diamonds or genie, then our hero will receive the punishment for making a false statement - Paradox. Surely, the only way to make sure that the integrity of the puzzle remains, and to avoid a paradox, is to make the statement true, for the one remaining true variable - i.e. giving away his daughter. ___ This is similar to the Pirate King of the Logical Positivists, who decrees that a certain empiricist is to be executed via the yardarm or the plank, depending on whether a statement he makes is true (he'll hang) or false (he'll drown). In [i]that[/i] puzzle, the empiricist has to render the entire problem logically impossible (by saying "I will drown"). In [i]this[/i] conundrum, he has to render most of the problem paradoxical, yet still leave one option within the puzzle open to him.
 Mon Mar 09, 2009 5:17 pm  by Jeffkins Similarly could he not say "You will give me Arlena's hand in marriage or you will put me to death." Essentially the reverse of rj82330's answer.