Math Riddles

Question: It takes ten men ten hours to build a certain wall. How long does it take five men to build the same wall?

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: Four people need to cross a bridge in 17 minutes in the middle of the night. The bridge can only hold two or less people at any time and they only have one flashlight so they must travel together (or alone). The flashlight can only travel with a person so every time it crosses the bridge it must be carried back. Tom can cross in 1 minute, John can cross in 2 minutes, Sally can cross in 5 minutes, and Connor can cross in 10 minutes. If two people cross together they go as fast as the slower person.How can they cross the bridge in 17 minutes or less?

Question: Tom wants to send Sally an expensive ring through the mail because they live thousands of miles apart. The only problem is that everything sent through the mail is stolen unless there is a lock put on it. Both Tom and Sally have plenty of locks and keys but they don't have any of the same locks or keys.

How can Tom send Sally the ring without it getting stolen?

Question: You have a bag with 'N' strings in it. You randomly grab two ends and tie them together until there are no more loose ends.

In the end, what is the expected number of loops (strings tied to their own end)?