Max Module Decomposition

Maximal Module Decomposition

A complex module was obtained by gluing together several cubes. You must identify a maximal module that generates a perfect decomposition of the original object (The original object can be reassembled from a number of maximal modules and nothing else).

For instance, given the object shown below,

one will find that a maximal decomposition is

Proposed Problem. Find a Maximal Module Decomposition of the following ensembles of cubes.

Watch the first part of the video. Pause when the message appears, find the solution and resume. One solution is presented in the second half of the video.

Note that the number of cubes in a maximal decomposition module should be a divider of the total number of cubes. In this case the number of cubes is 76.  Therefore, the maximal candidate is a 19-cube ensemble.

A second idea that can be followed is to investigate symmetric properties. In this case, this idea does not help.

Another hint you should consider is to think how you can prove your solution is correct. Well, it will suffice to compose the initial object using a specified number of copies of the module you proposed.