Math Riddles


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.

Question: A man wants to have a party in thirty-one days where he will be serving his 1000 barrels of wine. The only problem is that one of his enemies poisoned one of the barrels. The poison kills any man who drinks any of the wine in about 30 days, give or take a few hours. The man has 10 plants that are also killed by the poison in 30 days and can be used to test the wine. How can identify the single poisoned barrel of wine?