Question

Number the 12 edges of a cube with numbers 1 through 12 in such a way that the sum of the three edges meeting at each vertex is the same for each vertex.

a. 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12
b. 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1
c. 6, 3, 8, 7, 11, 2, 9, 5, 10, 1, 12, 4
d. 4, 9, 2, 7, 5, 11, 8, 3, 10, 1, 12, 6

Answer 1

To number the 12 edges of a cube in such a way that the sum of the three edges meeting at each vertex is the same for each vertex, the correct numbering is d. 4, 9, 2, 7, 5, 11, 8, 3, 10, 1, 12, 6.

Step-by-step explanation:

To number the 12 edges of a cube in such a way that the sum of the three edges meeting at each vertex is the same for each vertex, we need to assign numbers to the edges such that the sum is constant for every vertex. From the given options, the correct numbering would be d. 4, 9, 2, 7, 5, 11, 8, 3, 10, 1, 12, 6. We can check that the sum of the three edges meeting at each vertex, such as vertex 1 with edges 4, 9, and 2, is equal to 15. This is also true for all other vertices.