Sponsored by: UGA Math Department and UGA Math Club Written test, 25 problems / 90 minutes Summary: Sponsored by: UGA Math Department and UGA Math Club Written test, 25 problems / 90 minutes November 18, 2006 WITH SOLUTIONS No calculators are allowed on this test. 10 points for a correct answer, 0 points for an incorrect answer, and 2 points for an answer left blank. 1 Easy Problems Problem 1. A straight line crosses an 8 by 8 chess board. What is the largest number of squares it can pass through (not just touch the boundary)? (A) 8 (B) 15 (C) 16 (D) 17 (E) None of the above Solution. There are a total of 14 interior lines, 7 vertical and 7 horizontal. Every time the line crosses from one square to another, it crosses at least one of these interior lines. There is also the starting square. Therefore, the line cannot pass through more than 1 + 14 = 15 squares. The number 15 is possible, by considering a line close to a main diagonal. Problem 2. The lion always lies on Mondays, Tuesdays, and Wednesdays, but always tells the truth on the other days. The unicorn always lies on Thursdays, Fridays, and Saturdays, but always tells the truth on the other Collections: Mathematics