Spatial Reasoning Math Example 2

Solution

1. 1
   Step 1: The $3\times3\times3$ cut gives $27$ small cubes. Categorise by position: corners, edges, faces, centre.
2. 2
   Step 2: Cubes with paint on exactly $2$ faces are the edge cubes (not at corners). A cube has $12$ edges; each edge has $1$ middle cube (total $3$ per edge minus $2$ corners $= 1$). So $12 \times 1 = 12$ edge cubes.
3. 3
   Step 3: Each edge cube touches exactly $2$ painted faces. ✓