Question

The following figure consists of 8 horizontal lines and 14 vertical lines. The goal of this problem is to count the number of rectangles (squares are a kind of rectangle, but line segments are not).

Let V be the set of all sets of two vertical lines, and let H be the set of all sets of two horizontal lines. Let R be the set of all rectangles in the figure. Define a function

f : R → V × H by

  

f

↦

({AB, CD}, {AC, BD}).

Compute |R|, the number of rectangles in the figure.

Answer 1

f(R) = ({AB, CD}, {AC, BD}) where R is an rectangle with vertices ABDC. We define f in another way, in below. And tge number of rectangle is 2548.