Count exposed faces in a stack

Paint every outside face of the assembled stack except the bottom resting on the ground. Faces touching another cube receive no paint. A face can be painted even when it is hidden from this viewing angle.

For each cube, start with six faces. Subtract one for each neighbouring cube that shares a face. Subtract one more if the cube rests on the ground. Cubes that meet only along an edge or at a corner do not cover a face.

A single ground cube has 6 − 1 = 5 painted faces. In a row of two, each cube loses one face to its neighbour and one to the ground: 6 − 1 − 1 = 4. Count qualifying cubes, not the total number of painted faces.

This stack has four ground cubes, A–D, and cube E directly above A. The layer plans show every cube, including the one partly hidden under E. The numbers in the plans are painted-face counts for the assembled stack.

A touches B, C and E, and rests on the ground: 6 − 3 − 1 = 2. B, C and D each touch two cubes and the ground, so each has 3 painted faces. Their exposed rear or side faces still count even if the picture hides them.

E touches only A, so it has 5 painted faces. The tally is one cube with 2, three with 3, and one with 5: five cubes accounted for. Exactly three cubes have three painted faces. Removing layers to inspect them does not add paint to newly revealed contact faces.

The new stack has a complete 2 × 3 ground layer and one extra cube above the middle cube of the back row. Every column is filled from the ground; the plan shows column heights, not painted-face counts.

Check the four ground corners, the two ground middle cubes and the upper cube separately. Keep the bottom unpainted. The linked practice currently opens in English.