A rectangular cube with sides measuring 4 cm, is made with 1 cm^3 blocks. Two straight tunnels of 4 cubes each are taken out. All exposed surfaces are painted including inside the tunnels. How many small cubes have been painted on exactly 3 faces?

Answer 1

The original cube has 8 corners; each of them will be painted of 3 faces. The question then is how many other cubes will be painted on 3 faces after the two tunnels are taken out.

The problem says that both tunnels are 4 cubes, so that means the tunnels do not intersect.

However, there are different ways to take out two non-intersecting tunnels of 4 cubes each, and they produce different numbers of additional faces that will be painted on 3 sides.

So the statement of the problem is not sufficiently precise to answer the question. But your answer should be 19