A model is built from 6 cubes. The top and bottom surfaces of the entire model are white. All other exterior vertical surfaces are painted grey. Internal faces are unpainted. How many grey faces does

The model consists of 6 cubes. The top and bottom surfaces of the entire model are white. All other exterior vertical surfaces are painted grey. Any internal faces (touching another cube) are unpainted.

Let's identify each cube and count its grey faces:

• Cube 1 (bottom left, under a top cube): Has 3 exposed vertical faces (Front, Back, Left). Its top is covered, its bottom is white, and its right face touches another cube. So, 3 grey faces.
• Cube 2 (bottom middle, under a top cube): Has 2 exposed vertical faces (Front, Back). Its top is covered, its bottom is white, and its left and right faces touch other cubes. So, 2 grey faces.
• Cube 3 (bottom middle, next to Cube 2): Has 3 exposed vertical faces (Front, Back, Right). Its top is exposed (white), its bottom is white, and its left face touches another cube. So, 3 grey faces.
• Cube 4 (bottom right): Has 3 exposed vertical faces (Front, Back, Right). Its top is exposed (white), its bottom is white, and its left face touches another cube. So, 3 grey faces.
• Cube 5 (top left): Has 3 exposed vertical faces (Front, Back, Left). Its top is exposed (white), its bottom touches another cube, and its right face touches another cube. So, 3 grey faces.
• Cube 6 (top right): Has 3 exposed vertical faces (Front, Back, Right). Its top is exposed (white), its bottom touches another cube, and its left face touches another cube. So, 3 grey faces.

From the analysis above, only Cube 2 has exactly two faces painted grey.
The number of cubes with exactly two faces painted grey is $\boxed{1}$.

2.

A shape with exactly one pair of parallel sides is a trapezium (also known as a trapezoid).

• Shape A: The top and bottom sides are horizontal, making them parallel. The other two sides are not parallel. Thus, Shape A has one pair of parallel sides.
• Shape B: This is a hexagon. None of its sides appear to be parallel to each other.