Logic Riddles

Question: You have three coins. One always comes up heads, one always comes up tails, and one is just a regular coin (has equal change of heads or tails). If you pick one of the coins randomly and flip it twice and get heads twice, what is the chance of flipping heads again?

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: A man runs into a bar and asks for a glass of water. The bartender pulls out a shotgun and yells at him. The man thanks the bartender, then walks out of the bar happily.

Why did the man thank the bartender?

Question: You have two buckets: one with only white marbles and one with only black marbles. The two buckets have the same number of marbles.

How can you rearrange the marbles to maximize your chances of grabbing a white marble from each?

Question: Mrs. Stotch is a fifth grade teacher. One of her students took her apple. Mrs. Stotch has narrowed the suspects down to Billy, Paige, and Tyler. Each of these students give these statements:

Billy: I didn't do it.
Paige: I didn't do it.
Tyler: Paige did it!

Mrs. Stotch knows that only one of the kids is telling the truth. Which one is telling the truth and who took the apple?