In a standard open net of a dice, 2 dots is opposite to 5 dots, 1 dot is opposite to 6 dots, and 3 dots is opposite to 4 dots. Which of the following adjacent dot combinations represents a valid closed dice?

Two positions of the same dice are shown. In the first position, the adjacent faces shown are 1, 2, and 6. In the second position, the adjacent faces shown are 1, 2, and 5. Which number is on the face opposite to 6?

A cube is painted on all faces and then cut into 27 smaller cubes of equal size. How many smaller cubes have exactly two faces painted?