Math Riddles

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: 2 men catch 2 fish in 2 minutes. At this rate, how many men could catch 500 fish in 500 minutes?

Question: A claustrophobic person gets on a train. The train enters a tunnel just as it is leaving the station.

Where is the best place for him to sit?

Question: In a certain society any time somebody commits a serious crime they must be shot at twice with a 6 bullet revolver. The revolver only has two bullets in it though, both of them right next to each other. They spin the revolver once and shoot the gun. If there was no bullet in that chamber they give the prisoner the option to either spin the chamber again or just shoot again. If the first shot is a blank, should the prisoner ask for the revolver to be spun or should they choose that it be shot again?

Question: There are three men and a judge. The judge has 5 hats. Three of them are red and two of them are white. The judge says "Close your eyes, I am going to place a hat on each of your heads, who ever can guess what color hat they are wearing can go free." Facts: 1. The three men are standing in a line facing the judge. Where person three can see person two, one and the judge. Person two can see person one and the judge, person one can see the judge. Person three opens his eyes first, then person two, then person one goes last. 2. Each person can hear the others response. 3. The additional 2 hats are not visible 4. Person one guesses correctly. Question: What color hat is person one wearing and how do you know?