How Many Rectangles Can You Make?

Riddler Express

You have four squares that you can place on a large, flat table. You can place the squares so that their edges align, but their interiors cannot overlap.

Your goal is to position the squares so that you can trace as many rectangles as possible using the edges of the squares. For example, if you had two squares instead of four, you could place the squares side by side, as shown below:

With this arrangement, it’s possible to trace three rectangles: the square on the left, the square on the right and the larger rectangle around both squares. How would you arrange four squares to get as many rectangles as possible? And what is this number of rectangles?

Solution

Arrange the four squares around a nonexistant square.

Answer

There are five 1x1 squares.

There are four 1x2 rectangles.

There are two 1x3 rectangles.

11

Rohan Lewis

2023.02.20

Code can be found here.