Problem:
A regular octahedron has eight equilateral triangle face with four faces meeting at each vertex. Jun will make the regular octahedron shown in the figure by folding the piece of paper below. Which number face will end up to the right of the shaded region
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Begin by observing that when folded, the sides labelled and form the bottom half of the octahedron. As such, the remaining four faces must make up the top half of the octahedron. From here, we have narrowed down our possibilities to and . We can see that will be the number to the left of the shaded region . This also gives us that is to the left of . Therefore, we know that the only remaining face, must be to the right of the shaded region .
Thus, is the correct answer.
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions