Logic Riddles

Question: You are my brother, but I am not your brother. Who am I?

Question: A rat is placed at the beginning of a maze and must make it to the end. There are four paths at the start that he has an equal chance of taking: path A takes 5 minutes and leads to the end, path B takes 8 minutes and leads to the start, path C takes 3 minutes and leads to the end, and path D takes 2 minutes and leads to the start.

What is the expected amount of time it will take for the rat to finish the maze?

Question: Thomas is traveling through Germany and stops at a store to use the bathroom. The only problem is he cannot tell which bathroom is for males and which is for females. He finds somebody to ask which is which, but Thomas doesn't speak German. The person he finds can understand English but can only speak and respond in German.

Thomas really has to go to the bathroom, so what two yes or no questions can he ask to figure out which bathroom is which?

Question: During what month do people sleep the least?

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?