A couple of friends of mine were discussing a problem concerning this shape:
Is it possible to assemble enough of these to form a cube?
I have discovered a lot of impossible positions but was not successful in creating something useful. We have managed to build a 12x12x4 tower with leftover blocks at the top, however.
Maybe someone here has any ideas on how to tackle this problem? My next steps would be to try and extend our 12x12x4 tower, and if that doesn't work, to write a program to search for solutions.