Practice!

Sample Problem

In the figure below, 35 small squares form a big rectangle. There are 2 stars, each on 1 square. Find the number of rectangles (including squares) containing the two stars.

  rectangles

Solution

There are 2 horizontal lines above both stars, 3 horizontal lines below both stars, 3 vertical lines to the left of both stars, and 4 vertical lines to the right of both stars. From each of these groups of lines, we must select 1 line. After 4 lines are chosen, their intersection is a rectangle/square that will contain both stars. This method works because we are ensuring in our line selection that the top, bottom, right, and left edges of the rectangle/square will all be outside of the region defined by the two stars. So there are 2 × 3 × 3 × 4 = 72 such rectangles.