The Perplexed Carpenter

There is a hole in the barn floor that is exactly two feet wide and twelve feet long. A carpenter has only a single piece of wood that is three feet wide and eight feet long.

How can the carpenter take his piece of wood and, making only one cut, divide it into two equal parts that will exactly cover the hole in the barn floor?

Visiting the Mall

Bill, Chuck, Sally, and Dave all went to the mall together last week and entered at the same set of doors between Lord & Taylor's and Abercrombie & Fitch.  Dave wanted to go to the information booth to find out if he could buy mall gift certificates, Bill was hungry and said he needed to get something to eat at the snack bar, and Sally and Chuck needed to use the restrooms.

Can you draw a line from each person to their destination so that no two lines touch or intersect?

How Many Queens on a Chess Board?

Can you place eight Queens on a chess board so that no Queen can be 'taken' by any of the other Queens?

There are several unique solutions (ie. not reversals or rotations).  For an additional challenge, find all the solutions.

Pigs in a Pen

How do you put nine pigs in four pens so that each pen contains an odd number of pigs?

Knot or Not?

One day Professor Egghead was taking a walk in the park behind his house and spied a cord of some sort lying on the path. From the distance that he was from the rope he couldn't see if it was knotted or not.

As he continued to approach the cord he wondered about the probability of the cord being a knot.

In what orientations would the cord be a knot and what is the probability that the cord was knotted?