Wednesday, November 30, 2011

Question Mark Cane

I recently started using StubleUpon. I confined my searches to the Logic category and ended up finding a riddle website. I was solving riddles for hours yesterday. Here are three of my favorites:

Riddle 1: You are on an island surrounded by natives and visitors. The natives always lie. The visitors always tell the truth. All natives and visitors answer yes and no questions with the words "da" and "ba" but you don't know which means yes and which means no. You wish to know the true answer to a yes/no question (for simplicity: let's say the question is: Is today Wednesday?) but you may only ask one person one question. How do you do it?

Riddle 2: You walk into a room with 3 primates in it. There's a chimpanzee holding two bananas, an orangutan holding a stick, and a gorilla holding nothing. Which is the smartest primate in the room?

Riddle 3: All violins in a certain city were produced by Esau or one of his sons, or by Jacob or one of his sons. The violins are labeled to reveal the identity of their maker. Esau and his sons always label their violins truthfully; Jacob and his sons always label their violins with falsehoods. As an example, collectors figured out that a violin labeled "This violin was not made by any son of Esau." was made by Esau Sr. The most desirable violins are so labeled that a connoisseur can tell that it must have been made by one of the fathers, either Esau Sr. or Jacob Sr., but cannot tell which. How might such a violin be labeled?

Answer 1: You ask this: "If I were to ask you 'Is today Wednesday?', would you say ba?" If the person responds ba, it is Wednesday. If they respond da, it is not Wednesday. Interestingly, you can obtain the truth without knowing whether you are speaking to a native or visitor and without knowing what ba and da mean.

Answer 2: You are. Hopefully.

Answer 3: There are multiple solutions. One is: This violin was made by Esau Sr or by one of Jacob's sons.

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