Math Riddles

Question: Everyday a peasant must pay the king one pound of gold and leave it on a collection plate in front of his house. Every morning a guard comes by to make sure he has put a pound of gold on the plate. The king collects the gold every six days from the plate. If the peasant only has one six pound block of gold, how can he make only two parallel cuts and still follow the kings rules each day?

Question: Sam has two sons named Nathan and Daniel, Daniel is exactly 5 years older than Nathan and Daniel was born on February 29th 1996. How old is Nathan?

Question: Two spies want to get in an enemy's military base. In order to get in they have to give the correct countersign to the guard at the gate after he gives them the sign. So, they wait hidden nearby the gate so that they will overhear the countersign from another soldier. One soldier comes and the guard gives the sign: "6". The soldier answers "3". The guard lets him pass. Another soldier comes. The guard says "12" and the soldier gives the answer "6". The guard lets him pass. So, the first spy goes at the gate and the guard says "10".The spy, sure that he knew the answer as he was, says "5". Immediately, the guard shoots him dead. Then the other spy, who saw that the other spy was killed when he gave the countersign, had now understood what the right answer would be, whatever the guard's sign was.So, he walks to the gate and the guard says "8".The spy gives the correct answer and the guard lets him in. What was the answer that the spy gave?

Question: A man goes into a barbershop and gets a $15 haircut. He pays the barber with a $20 bill, but the barber doesn't have change because it is an especially slow day. The barber goes to the flower shop next to his own and trades the $20 bill for a $10 dollar bill and two $5 bills. Then he gives the man his $5 in change.

Later the lady from the flower shop confronts the barber and tells him that the $20 bill he gave her was counterfeit. The barber agrees and he gives the lady a different $20 bill.

Later that day he tries to figure out how much money he lost. What did he lose?

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?