Cube Container House

To build a qualified cube container house with the minimum number of building modules, at least 18 modules are required. The detailed analysis is as follows:

Module Combination Rules and Objectives

The problem requires the use of both cube and rectangular prism modules to construct the container house. Each module must have a window, and the window's face must not coincide with the face of any other module. Additionally, windows must not face the sky, meaning they must face the external space of the container house. Moreover, the window directions of modules on the same layer must be staggered to avoid overlap. The objective is to achieve a structure that meets the layer requirements in the top-down view using the minimum number of modules.

Top-Down View Layers and Module Splitting Logic

According to the top-down view, the container house consists of 5 layers, with the number of modules per layer decreasing from bottom to top:

• Layer 1 (Bottom Layer): A total of 7 modules, corresponding to positions where the total number of layers in the top-down view is ≥ 1.
• Layer 2: A total of 5 modules, corresponding to positions where the total number of layers is ≥ 2.
• Layer 3: A total of 4 modules, corresponding to positions where the total number of layers is ≥ 3.
• Layer 4: A total of 1 module, corresponding to positions where the total number of layers is ≥ 4.
• Layer 5 (Top Layer): A total of 1 module, corresponding to positions where the total number of layers is = 5.

By retaining only the modules that meet the layer requirements at each level, structural stability can be ensured, while window directions can be adjusted by orienting modules outward to avoid overlap.

Calculation of the Minimum Number of Modules

Summing up the number of modules at each layer:
7 (Layer 1) + 5 (Layer 2) + 4 (Layer 3) + 1 (Layer 4) + 1 (Layer 5) = 18 modules.
This solution optimizes module stacking to avoid redundant modules, such as not repeatedly placing modules in intermediate layers that only support local parts of the upper layers, thereby minimizing the total number of modules.

Module Selection in Practical Applications

In actual construction, cube modules (such as 20-foot or 40-foot containers) are often preferred due to their standardized dimensions and structural stability. Rectangular prism modules may be used to fill spaces or adjust window directions. However, since the problem does not limit the proportion of module types, the combination of 18 modules can consist entirely of cube modules or flexibly incorporate rectangular prism modules based on window direction requirements.