Fit rectangles

Was wondering if someone could help with a simple problem.

I have a 70x20 rectangle, and I want to fit as many smaller rectangles (A, B, C) in it as possible.

The sizing of the smaller rectangles is as follows:

A = 2x3

B = 4x4

C = 8x9

The quantity and arrangement of these rectangles is based on some rules:

For every B rectangle there needs to be five A rectangles.
There are four C rectangles, regardless.
The A rectangles need to be touching the perimeter of the 70x20 perimeter.
All rectangles are oriented orthogonally (either 0 deg or 90 deg).

I have a feeling that there are many possible combinations, but maybe someone can shed light onto this puzzle. How can the combinations be determined quickly?

Cheers!

Replies to This Discussion

Permalink Reply by Omar Helmy on October 3, 2012 at 2:01pm

Can u do a sketch to explain what you wanna achieve?

Permalink Reply by Alejandro on October 3, 2012 at 4:20pm

Here's a quick sketch.

As I was sketching, I noticed that there would be a lot of space between the 2x3 rectangles and the big 8x9 ones, so I decided to see what it would look like if I paired the 2x3s into clusters instead.

Can the clustering of rectangles be a parameter? It would be nice to know how much clustering is required to make better use of the available space.

This is a learning exercise, so I think that maybe some of the constraints will not be known until later on.

Permalink Reply by Omar Helmy on October 4, 2012 at 7:32am

i think u might wanna look into using Galapagos, i did something like that a while ago. Let me find u the script...

Permalink Reply by Jonah Hawk on October 4, 2012 at 3:23pm