On Sep 8, 2006, at 8:13 PM, Oliver Stemforn wrote:
> Let the n by n dots be in one plane, and let n be equal to or > greater than 2. Rectangles here are understood to be squares or > non-square rectangles. A rectangle counts only when each of its > four vertices coincides with one of the dots of the array.*** > > Can you come up with a polynomial in terms of n for the total > number of rectangles for a general n by n array?
You are going to have to be more careful about when a rectangle counts. Must the sides be horizontal/vertical? Or does the rectangle formed by, say, (0,7), (4,10), (10,3), (6, 0) count when n = 10? If so, the problem may be considerably more difficult than you thought
--Lou Talman Department of Mathematical and Computer Sciences Metropolitan State College of Denver