Problem:
How many pairs of parallel edges, such as and or and , does a cube have?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Each of the edges is parallel to other edges giving possible pairs of parallel edges. But each pair of parallel edges is counted twice in this process, so there are pairs of parallel edges.
There are pairs of parallel edges related to , . Similarly there are pairs of parallel edges related to and pairs of parallel edges related to for a total of pairs of parallel edges.
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions