This same proof technique is the primary method for identifying impossible configurations for the Soma Cube puzzle: https://en.wikipedia.org/wiki/Soma_cube htt

This same proof technique is the primary method for identifying impossible configurations for the Soma Cube puzzle: https://en.wikipedia.org/wiki/Soma_cube https://en.wikipedia.org/wiki/Soma_cube "Seven pieces made out of unit cubes must be assembled into a 3×3×3 cube. The pieces can also be used to make a variety of other 3D shapes."