Extreme Beginner Question - Separating... Layers?

I'm a complete newcomer to Grasshopper so I have very little know-how on what I'm doing.

This is probably a really simple problem, but I have no idea how to approach it.

I'm trying to create a checkerboard pattern box type object. Basically a box with individualized layers with alternative cull patterns so that every other layer will be the same cull pattern, and then using T-box to make smaller boxes from the cull patterns inside the larger box.

If that didn't make much sense, here is an image of what I have so far and what I'm trying to achieve.

 

http://i.imgur.com/A337w.jpg

I've also attached the short gh file.

Basically - how do I delete every other layer for each box pattern?

Thank you for any help!