7.2. Petya says to Kolya: «I placed some numbers at the vertices of a cube, and then on each face I wrote the sum of the four numbers at its vertices. Then I added all six numbers on the faces and got 2019. Can you figure out what the sum of the eight numbers at the vertices of the cube is?» How would you answer this question if you were Kolya?
Answer: 673. Solution. Each vertex of the cube belongs to three faces (which meet at this vertex) and therefore the number placed at this vertex participates three times in the calculation of the sums on the faces. Thus, the sum of the numbers at the vertices is $2019: 3=673$. Comment: another way to solve (direct) is as follows: by denoting the 8 unknown numbers at the vertices of the cube and expressing through them the sum of the numbers on the faces, after factoring out the threes, in parentheses we will get the sum of all the numbers at the vertices.