Math Riddles

Question: If you have a cake, how many pieces of cake can you form with 3 straight cuts?

Question: A knight comes to a castle where his love is trapped. The castle is surrounded by a square moat that is 10 feet wide (it forms a square around the castle). The knight is able to fashion two 9 foot long planks to cross the moat.

How can he do this?

Question: Ants on a stick may only move left or right. If they bump into each other they bounce off of each other and immediately move in the opposite direction maintaining speed the entire time. The only time they change speed is when they fall off of the edge of the stick.

If 25 ants are randomly put on a 1 meter long stick moving 1 meter per second, what is the longest amount of time it could take for them to all fall off?

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)?

Question: You have two books. One of them is upside-down and the other is rotated so the top of the book is facing you.

What is the sum of the first page in each book?