Two identical very thing rings. One lays flat on a table and the other stands inside it. They touch at four points. If the inner ring just touches the table, give the rings' ratio of diameter to width.
If you have two identical screws and arrange them such that their threads touch each other with their heads facing away from each other. Screw one screw and unscrew the other. What happens?
There are 6 students to be seated around a circular table. In how many ways they can be seated if two particular persons are next to each other.
Three points are selected at random on a sphere's surface. What is the probability that they all lie in the same hemisphere? Assume that the great circle, bordering a hemisphere, is part of the hemisphere.
