Math Riddles

Question: On a clock, how many times a day do the minute and hour hand overlap?

Question: You find me behind the stars; or in a sixth, seventh, or third.
It takes something round, a computer, and me to make pie.
I am bigger than anything you can think of.

What am I?

Question: Joe deals himself and his friend John some cards from a deck of cards (not the same amount). If John gives Joe some cards Joe will have 4 times as many cards as John. If Joe gives John the same number of cards he will have 3 times as many cards as John.

How many cards does each man have and how many cards do they trade?

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?

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?