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Very Difficult Logic Problems
Sultan and his princess
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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.
Tue Nov 30, 2010 9:13 pm  by Trenin

How about this:
"You will give me none of those three things, or you will give me your throne and I will forfeit my right to ask for a prize."

To analyze this, it is basically two clauses - A or B - where:
[list]A is "You will give me none of those three things"
B is "You will give me your throne and I will forfeit my right to ask for a prize"
[/list:u]By making any one of them true, the entire statement is true.

Lets suppose the sultan decides this statement is false. Then he gives the young man nothing and kills him. This makes clause A true, thus the entire statement is true, which is a contradiction.

Thus the statement must be true.

The first clause A can't be the only one that is true because then the sultan must give the young man a prize of the sultan's choosing if the young man wishes it (which he would) which makes clause A false - another contradiction.

Thus the second clause B must be true - the sultan is forced to give up his throne. Some of you may say this is still a contradiction because if the statement is true, then the sultan must give the young man a prize. However, the wording of the puzzle is:

If the statement is true, you [i][b]may[/b][/i] have one of the following three things, but I get to choose!

Thus, it is up to the young man if he wants to get a prize, but it is up to the sultan which prize. Thus, the young man can refuse the prize and not have a contradiction. He does this explicitly in his statement, thus making the way clear for what the sultan must do.

When the young man takes the throne, he then takes not only the princess' hand in marriage, but everything else in the power of the sultan as well.
Sun Feb 24, 2013 7:37 am  by kattavijay

king will not give him three things and he will not give him throne and he will just kill him. whats wrong in this
Sun Feb 24, 2013 7:47 am  by kattavijay

king may give him diamonds and kills him.
clauseA becomes wrong , Clause B is also wrong , so he can be killed for wrong statement. King can give diamonds even he has given
wrong statement
Thu May 09, 2013 9:34 pm  by treerex

Wily makes the following statement...

"You will be my father in law."

If sultan considers this as false then Wily is allowed to choose to marry the princess and that makes the statement as true. If statement is true then there is no option for sultan but to accept the marriage proposal. In any case, Wily will have his way.
Fri Oct 10, 2014 12:55 am  by Decius

"You will either be my father in law or put me to death"

The second clause makes false->execution->true (a contradiction), while the first makes any lesser reward false->reward (a contradiction).
Sat Feb 28, 2015 4:09 pm  by hemant.bisht24

you will neither give me diamonds nor magic lamp
Mon Aug 10, 2015 3:30 pm  by Nesan135

I can see that a lot of people are confused by this question and have misconceptionalized it.

The most reasonable statement to make is : " I will accept any of the rewards that you choose for me and I will use it to come after your throne if and only if the reward that you choose to give me is not your daughter's hand in marriage. ".

This will instill fear in the Sultan as he might potentially lose his throne if the witty man were to acquire an army by offering the valuable diamonds to another King to destroy the Sultan or by wishing from the genie , an unstoppable army to destroy the Sultan and his kingdom.

Hence , the Sultan will have no other choice but to offer his daughter's hand in marriage to avoid being dethroned and killed by the witty man.

Note : This explaination is for if the Sultan takes the witty man's statement as a true statement.

The Sultan will not be able to say that the witty man's statement is false because a statement is judged to be true or false using mathematical reasoning using the " p if and only if q" and " if q then p " as follows :

" I will accept any of the rewards that you choose for me and I will use it to come after your throne if and only if the reward that you choose to give me is not your daughter's hand in marriage.".

If it is reversed,

" If the reward that you choose to give me is not your daughter's hand in marriage then I will accept any of the rewards that you choose for me and I will use it to come after your throne.".

Hence , no paradox and no contradictions.
Tue Feb 16, 2016 10:48 am  by MikeofClubs

I will marry your daughter if and only if my statement is true.
Wed Apr 06, 2016 12:37 pm  by vikrantsach

"You are going to kill me".. After this sentence Sultan neither prove this answer wrong by killing him nor it will be true as Sultan could not kill him hence Sultan have to give up and act as per his wish.. :D
Wed Jul 13, 2016 6:16 am  by Dzallen

Nesan135, I still believe your statement can be considered false, i.e. the sultan can say that "if the reward I choose for you is not my daughter's hand in marriage, then you will not accept any of the rewards that I choose for you and use it to come after my throne"

the statement is considered false if either "I will accept any of the rewards" is false, or the more likely "I will use it to come after your throne" is false. The sultan can argue that the second part is false by, for example, stating that he 'would' put the man in prison, making him unable to come after his throne, if he receives his gifts.

MikeofClubs, your statement "You will give me your daughter if and only if my statement is true" is true regardless of whether the Sultan gives his daughter, hence he could receive any gift.

As others have posted, the statement to make must create a paradox if he receives either of the two other gifts, e.g. "I will not receive the Diamonds or the Genie" or "I will be put to death or receive your daughter as a bride"
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