Problem:
A cube has eight vertices (corners) and twelve edges. A segment, such as , which joins two vertices not joined by an edge is called a diagonal. Segment y is also a diagonal. How many diagonals does a cube have?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
There are two diagonals, such as , in each of the six faces for a total of twelve face diagonals. There are also four space diagonals, such as , which are within the cube. This makes a total of .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions