¶ 2024 AMC8 Problem 20
Problem:
Any three vertices of the cube , shown in the figure below, can be connected to form a triangle. (For example, vertices , , and can be connected to form isosceles .) How many of these triangles are equilateral and contain as a vertex?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
We first note that we can only form equilateral triangles if we go through the diagonals of the square faces; otherwise, at least one angle of the triangle will be different. Afterwards, it is easy to exhaust all possible equilateral triangles that can be formed:
Thus, is the correct answer.
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions