Question 2
There are 27 unit cubes, each of size $1\times1\times1$, are glued together to form a larger $3\times3\times3$ cube. Each face on each of the $1\times1\times1$ unit cubes contains a positive integer such that:
(i) Two opposite faces of any unit cube must always contain an even number and an odd number. Moreover, the even number must be twice the odd number.
(ii) When any two unit cubes are placed face-to-face, the two touching faces must always contain an even number and an odd number. Moreover, the odd number must be 1 more than the even number.
(a) Place the numbers in the faces of $A'$, $B'$ and $C'$ which are opposite to the faces of $A$, $B$, and $C$, respectively. Find the total sum of the numbers on the faces of $A'$, $B'$ and $C'$. (2 Marks)
(b) Find the total sum of the numbers on the faces of all the unit cubes. (4 Marks)
(i) Two opposite faces of any unit cube must always contain an even number and an odd number. Moreover, the even number must be twice the odd number.
(ii) When any two unit cubes are placed face-to-face, the two touching faces must always contain an even number and an odd number. Moreover, the odd number must be 1 more than the even number.
(a) Place the numbers in the faces of $A'$, $B'$ and $C'$ which are opposite to the faces of $A$, $B$, and $C$, respectively. Find the total sum of the numbers on the faces of $A'$, $B'$ and $C'$. (2 Marks)
(b) Find the total sum of the numbers on the faces of all the unit cubes. (4 Marks)