Good Riddles

Riddle #99 (hard)

Question: How many people do you need to have the odds be in favor (at least 50% chance) of two people having the same birthday?

Question: A man is stuck on an island with his best friend and a fisherman. The fisherman and his best friend go off to catch food while he builds a hut. The fisherman returns alone with some salmon he had prepared. His best friend had fallen off a cliff.

After he is rescued from the man goes to a diner and he orders salmon. He eats his meal, he pulls out a gun and commits suicide. Why does he do this?

Question: There is a basket full of hats. 3 of them are white and 2 of them are black. There are 3 men Tom, Tim, and Jim. They each take a hat out of the basket and put it on their heads without seeing the hat they selected or the hats the other men selected. The men arrange themselves so Tom can see Tim and Jim's hats, Tim can see Jim's hat, and Jim can't see anyone's hat.

Tom is asked what color his hat is and he says he doesn't know.
Tim is asked the same question, and he also doesn't know.
Finally, Jim is asked the question, and he does know.

What color is his hat?

Question: If you have an 11 minute and 13 minute hourglass, how can you accurately time 15 minutes?

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.