Logic Riddles

Question: A king finds a woman he wants to marry but she refuses. But since he is the king, she has to. The king gives her a deal: he will write 'YES' and 'NO' on two pieces of paper. The papers will be put into a hat and she will choose one. If it says yes she will marry him, if it says no she will not. The only problem is that the king cheats and puts two pieces of paper that say yes into the hat, but the woman is the only one who sees this.

How can the woman avoid marrying the king?

Question: If you have a rope around a soccer ball and the moon, which rope would have to increase in length more to create a one meter gap between the rope and the soccer ball/moon?

Question: A man taking the census walks up to the apartment of a mathematician and asks him if he has any children and how old they are. The mathematician says "I have three daughters and the product of their ages is 72." The man tells the mathematician that he needs more information, so the mathematician tells him "The sum of their ages is equal to our apartment number." The man still needs more information so the mathematician tells him "My oldest daughter has her own bed and the other two share bunk beds."

How old are his daughters?

Question: There are 1600 people sitting around a circular table. The first person (person 1) has a sword and kills the second person then hands it to the next alive person (in this case person 3). Person 3 stabs person 4 and gives the sword to person 5. This goes on until person 1499 kills person 1500. Then person 1 kills person 3 and so on. This is repeated until there is only a single person remaining.

Who remains in the end?

Question: A prison has 23 prisoners in 23 different cells. The prisoners have no way to communicate with each other in any way from their cells. There is another room, the rec room, that has two switches on the wall (A and B). The switches have on and off positions but they start in an unknown position.

Prisoners are randomly taken to and from the rec room one at a time. They must change the position of only one of the two switches each time they go to the room. At any point a prisoner can yell out, "Every prisoner has been here!" If the prisoner is correct that all of the prisoners have visited the rec room, then they all go free. If they aren't correct then they are all executed.

Before they start they are given one planning session during which they can discuss a method to win the game. What method can they use to ensure they all go free?