+13 I’ll interpret your question as follows. You have an n×n grid of n2 cells. You’ve got one color. Each square can be either colored or left uncolored. (I’ll use 0 for uncolored and 1 for colored.) How many ways can the cells be colored so that no two rows have the same number of colored cells and no two columns have the same number of colored cells. www.mywawavisit.com
+13 I am assuming that the four (or n) points are considered in the order that they appear on the circle rather than the order in which they were chosen. (Otherwise, the quadrilateral [polygon] might not be “proper.”) The event “the polygon contains the center of the circle” is equivalent to the event “every diameter of the circle intersects the polygon,” so it is the complement of the event “all n points fall on one side of some diameter of the circle.” PartyCityFeedback Survey