Problem 5.6. There are 4 absolutely identical cubes, each of which has 6 dots marked on one face, 5 dots on another, ..., and 1 dot on the remaining face. These cubes were glued together to form the figure shown in the image.

How many dots are on the four left faces?

![](https://cdn.mathpix.com/cropped/2024_05_06_ddcc40423d5e6a42b0ccg-10.jpg?height=505&width=299&top_left_y=95&top_left_x=579)

- The number of dots on face $A$ is ...
- The number of dots on face $B$ is ...
- The number of dots on face $C$ is ...
- The number of dots on face $D$ is ...
Answer: On face $A$ there are 3 points, on face $B-5$, on face $C-6$, on face $D-5$. Solution. Let's consider the arrangement of the faces on one die. We will denote the faces by numbers corresponding to the number of dots on them.

From the picture, it is clear that face 1 borders with faces $2,3,4$ and 5. Therefore, opposite to it is face 6.

Face 2 borders with 4 and 5 (as well as with 1). Thus, the neighbors of face 1 are arranged around it in the order 2, 5, 3, 4, which means that faces 4 and 5 are opposite. The remaining two faces, 2 and 3, are also opposite.

![](https://cdn.mathpix.com/cropped/2024_05_06_ddcc40423d5e6a42b0ccg-10.jpg?height=474&width=519&top_left_y=1277&top_left_x=467)

Now it is not difficult to understand that on face $A$ there are 3 points, on face $B-5$, on face $C-$ 6, on face $D-5$.