[ Cube

Can the numbers from 1 to 12 be placed on the edges of a cube so that the sums of the numbers on all faces are the same?

#
On the cube $A B C D A_{1} B_{1} C_{1} D_{1}$, we will place numbers as follows:

$A B-10, B C-5, C D-7, A D-4$,

$A_{1} B_{1}-3, B_{1} C_{1}-9, C_{1} D_{1}-6, A_{1} D_{1}-8$

$A A_{1}-2, B B_{1}-11, C C_{1}-1, D D_{1}-12$

On each face of the cube, the sum of the numbers is 26.

## Answer

It is possible.