September's problems:

1. In how many ways can a dollar be changed into a combination of quarters, dimes, nickels, and pennies?
2. Set up a system of bus lines such that every bus has exactly three stops, every stop lies on exactly three lines, and there is one and only one bus joining any two stops.
3. At a conference dinner 100 mathematicians in a round table decide to settle the bill in the following unusual way: they number themselves 1,2,...,100 in clockwise order and give the bill to number one. Number one gives the bill to number three and leaves. Number three gives the bill to number 5 and leaves, and they continue in this fashion passing the bill to every second person until there is only one mathematician left and she has to pay the bill. What number was the unlucky person? Give a formula for the case when we have n mathematicians.
4. Draw any finite number of lines on the plane. Show that the regions into which these lines divide the plane can be colored with two colors in such a way that any two adjacent regions have different colors.
5. A region in the plane is said to be convex if every two points in the region are joined by a line segment completely contained in it. A region in the plane is said to be bounded if it can be enclosed in some disc. Show that an unbounded convex region in the plane must contain a half-line.
6. Prove that, independently of his initial position, a knight may move to all the squares of a chessboard.