How To (Maybe) Marry A King's Daughter
You are on an island where there are three types of people: TRUTHERS who always tell the truth, LIARS who always lie, and ORDINARY people who sometimes tell the truth and sometimes lie. The King has decreed that his daughter must marry only an ORDINARY person.
As it happens, you are an ORDINARY person, and you and the King's daughter have fallen in love with each other. The King will permit you to marry her if you can pass a test. He is an excellent logician. If you can make a single statement that meets two conditions, you can marry the daughter.
1) Your statement must prove to the King that you are an ORDINARY person.
2) Your statement must make it impossible for the King to determine whether it is true or false.
Is it possible to make a single statement that is guaranteed to win you the King's daughter?
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3 solutions
Moderator note:
Nice solution to this problem. Remember that only ordinary people can say that they are liars.
Take a condition that is unknown to the King. For example, that you have exactly one seashell in your back pocket.
Then state: "Either I am an ORDINARY person who is carrying exactly one seashell in my back pocket, or else I am a LIAR."
A TRUTHER couldn't say that, because they are neither ORDINARY nor a LIAR.
A LIAR couldn't say that, because then they would be telling the truth about being a LIAR.
So you must be an ORDINARY person. But the King cannot know whether your statement is true or false, because he does not know how many seashells you have in your back pocket.