Problem:
An insect lives on the surface of a regular tetrahedron with edges of length 1 . It wishes to travel on the surface of the tetrahedron from the midpoint of one edge to the midpoint of the opposite edge. What is the length of the shortest such trip? (Note: Two edges of a tetrahedron are opposite if they have no common endpoint.)
Answer Choices:
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Solution:
Unfold the tetrahedron onto a plane. The two opposite-edge midpoints become the midpoints of opposite sides of a rhombus with sides of length 1 , so are now unit apart. Folding back to a tetrahedron does not change the distance and it remains minimal.
The problems on this page are the property of the MAA's American Mathematics Competitions