Step-by-Step Analysis

To solve this puzzle, we need to determine the size of the large cube and then consider how its placement on a table affects the visibility of the smaller cubes' faces.

1. Determine the Cube's Dimensions

The large cube is made up of 125 smaller cubes. If the side length of the large cube is 'n' small cubes, its volume is $n^3$.

$n^3 = 125$

$n = \sqrt[3]{125} = 5$

So, we are dealing with a 5 × 5 × 5 cube.

2. Identify Cubes with Three Exposed Faces

In any cube, the smaller cubes with three faces exposed are always the corner pieces. A standard cube has 8 corners.

3. Consider the "Placed on a table" Constraint

The problem states the cube is placed on a table. This means the entire bottom face of the large cube is hidden and not visible.

• Top Corners: The 4 corners on the top of the cube have three faces visible (the top face and two side faces).
• Bottom Corners: The 4 corners at the bottom are resting on the table. Their bottom face is hidden. Therefore, they only have two faces visible (the two side faces).

Conclusion

The question asks for the number of cubes with exactly three sides visible. Based on our analysis, only the 4 top corners of the cube meet this condition.

Therefore, the number of squares (faces of the small cubes) visible only on three sides is 4.