Problem:
Given the nine-sided regular polygon , how many distinct equilateral triangles in the plane of the polygon have at least two vertices in the set ?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Each of the pairs of vertices determines two equilateral triangles, for a total of 72 triangles. However, the three triangles , , and are each counted 3 times, resulting in an overcount of 6 . Thus, there are distinct equilateral triangles.
The problems on this page are the property of the MAA's American Mathematics Competitions