10.3. Numbers $1,2,3,4,5,6,7$ and 8 are placed at the vertices of a cube, such that the sum of any three numbers belonging to any face is not less than 10. Find the minimum possible sum of four numbers belonging to one face.
Answer: 16. Evaluation. Consider an arbitrary face. If the largest number written at the vertex of this face is no more than 5, then the sum of the remaining numbers is no more than $4+3+2=9$. Therefore, the largest number written at the vertex of any face is at least 6, and the minimum possible sum of four numbers belonging to one face is at least 16. An example is shown in the figure, where the minimum sum is on the "near" face.

![](https://cdn.mathpix.com/cropped/2024_05_06_0227d4b25387ca8dcc37g-3.jpg?height=446&width=419&top_left_y=2147&top_left_x=1458)

Comment. Answer without an example - 1 point, example - 2 points, evaluation without an example - 3 points. Answer, example, and evaluation - 7 points.