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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

  

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

 

Collections: Mathematics