Problem:
The numbers on the faces of this cube are consecutive whole numbers. The sums of the two numbers on each of the three pairs of opposite faces are equal. The sum of the six numbers on this cube is
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Since , and are on five of the faces, the number on the remaining face must be or . In the first case, must be on the face opposite the face with which is impossible since would force and to be on opposite faces. Thus is opposite is opposite , and is opposite . The sum on each pair of opposite faces is , and the desired sum, is .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions