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

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