Math Riddles

Question:

John has some chickens that have been laying him plenty of eggs. He wants to give away his eggs to several of his friends, but he wants to give them all the same number of eggs. He figures out that he needs to give 7 of his friends eggs for them to get the same amount, otherwise there is 1 extra egg left.

What is the least number of eggs he needs for this to be true?

Question:

You have a large number of friends coming over and they all get thirsty. Your first friend asks for 1/2 a cup of water. Your second friend asks for 1/4 a cup of water. Your third friend asks for 1/8 a cup of water, etc.

How many cups of water do you need to serve your friends?

Question: What is 1/2 of 2/3 of 3/4 of 4/5 of 5/6 of 6/7 of 7/8 of 8/9 of 9/10 of 10,000?

Question: John has been hired to paint the numbers 1 through 100 on 100 apartments.

How many times with he have to paint 8?

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?