All Models of 2x4 LEGO Bricks

Motivation

Previous results count all the ways that 2x4 LEGO bricks can be connected at straight angles.

Bricks connected at right angles
There are 915.103.765 ways to combine 6 bricks at straight angles.

We seek to find the number of ways up to six bricks can be connected when using all possible angles.

Bricks connected at odd angles
It is currently unknown how many ways 6 bricks can be combined at other angles.

Our Findings

For an explanation of the terms used in this section, please refer to the Terminology section below.

This is a work in progress, so the results are still incomplete. The tables below shows the current findings. The numbers marked with an asterix (*) are not yet final.

Number of bricks 1 2 3 4 5 6
RC's (previous results) 1 24 1.560 119.580 10.166.403 915.103.765
Models (our main results) 0 0 0 1.144 213.221* 26.417.316*

See the detailed findings page for a breakdown of these numbers, or go directly to the models page so see the models. The full paper is currently under construction, and will contain all details of the theory behind the numbers, as well as the software used to find them.

Terminology

In this section we define the terms used in the table of our current findings above.

Models
These configurations all belong to the same model.

We typically use colors to highlight the individual sub-configurations that can be turned. This is, however, only for illustrative purposes. Our results, as well as previous results, assume that all bricks have the same color and are thus interchangeable.

What now?

If you have read the terminology above and want to see more details, then the findings page is the place to continue. If you want to see what the software has found, then you might appreciate the SCC and models pages. The full paper is currently under construction, and we are working on improving the algorithm to find models using the software. The GitHub project is open for ideas of improvement.

Contact

Lasse Deleuran can be contacted at e-mail lassedeleuran@gmail.com. For any issues with the code, please use the issue list on GitHub.