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 Collections: Mathematics