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Sponsored by: UGA Math Department, UGA Math Club, UGA Parents and Families Association
 

Summary: Sponsored by: UGA Math Department, UGA Math Club,
UGA Parents and Families Association
Team Round / 45 minutes
WITH SOLUTIONS
No calculators are allowed on this test. You do not have to provide
proofs; only the answers matter. Each problem is worth 50 points, for a total
of 200 points.
Problem 1. (Crawling Ant) An ant is crawling on a surface of a rectan-
gular box with sides 9, 10, and 11 cm (see the picture). What is the smallest
distance it must crawl to get from one corner to the opposite corner, farthest
from the first one?
Answer.

482
Solution. Call the sides of the box a, b, and c. Clearly, the ant should use
no more than two sides of the box. We can then fold these two sides and
put them on the plane to obtain a rectangle with sides a + b and c (see the
picture). Then shortest path from one corner of this rectangle to another is
the diagonal, and its distance is d, where
d2

  

Source: Alexeev, Valery - Department of Mathematics, University of Georgia

 

Collections: Mathematics