Math Riddles

 
Half his Age (medium)

Question: When Tommy was 10 years old his sister Suzy was half his age. Now that Tommy is 50 years old how old is his sister Suzy?


Question: Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a sports car; behind all of the others is bicycles. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 2, revealing a bicycle. He then says to you, "Do you want to pick door No. 3?" Is it to your advantage to switch your choice?

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: 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.