Question

Dice are cubes with dots on each face. Opposite faces of a die always have a total of seven dots on them. Here are two nets to make dice (cubes); the numbers inserted in each square indicate the number of dots in that box. Insert suitable numbers in the blanks, remembering that the number on the opposite faces should total to 7.

Answer 1

Hint: To solve this question, one needs to know the basics of the net pattern of the cube and how it can be rearranged to give back the cube. Further, we also make use of the property that opposite faces should total to 7 to find the solution to this problem.
Complete step-by-step answer:
For the solution, we will refer to the below figures.

The task is to find the suitable blank numbers. In this case, we have to find a, b, c, d, e and f from both the above nets. Let us start with the net pattern of the cube to the left. We have to find the appropriate folds which would result in the formation of this net back into the cube. Thus, to do that, we would have to fold from the place between the face containing 4 and the face containing c (which we have to find). If we rearrange the fold carefully, we would get the lateral surfaces (surfaces excluding top and bottom) which would have the faces b, c, 4 and 5. Here, b would be opposite to face containing 4 and c would be opposite to the face containing 5. The top faces would be face containing a and 6 respectively. Thus, since sum of opposite faces should be 7, we have,
b + 4 =7
b = 3
a + 6 = 7
a = 1
c + 5 = 7
c = 2
Hence, the missing faces are a = 1, b = 3, c = 2 (according to the figure).
In the second figure, we have, to make a fold from between the faces e and f first, then between faces e and d (then close the d surface down such that it becomes the top surface to face e). We then fold the face 3 such that it is now opposite to the face f. As we make this fold, face 1 would be opposite to the face e. Thus, face 2 would be opposite to the top face d. We have,
3 + f = 7
f = 4
e + 1 =7
e = 6
2 + d =7
d = 5
Hence, the missing faces are d = 5, e = 6, f = 4 (according to the figure).

Note: For solving the problems related to the net pattern of a solid shape, a good amount of visualisation is required (as can be seen in this problem). One can also try to cut a net pattern representing the above figures from a paper and then try to form the cube from the paper by hand to gain better understanding.