Logic Riddles

Question: In what year did Christmas and New Year's fall on the same year?

Question: A woman is in the hospital for a routine procedure. The doctor leaves the room locking the door before he goes, the woman is alone. The doctor comes back to find the woman has died and there is another person is in the room. The door was still locked.
How is this possible?

Question: You have a glass of water that looks about half full. How can you tell, only using the glass of water itself, if the glass is half full or not?

The glass is a right cylinder.

Question: There are 2 fathers and 2 sons going on a fishing trip. Every person catches one fish. In total, there were only 3 fish. How is that so?

Question: There are two ropes that both take exactly 1 hour to burn from end to end. You are unable to cut the rope. How can you burn the two ropes in a total of 45 minutes?