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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
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. The star below is drawn on the standard rectangular grid on
which every square has size 1 by 1. What is the area of the star?
(A) 26.5 (B) 27 (C) 27.5 (D)
28 (E) None of the above.
Solution. First way. Just cut into triangles and count their areas separately.
Second way. Use Pick's formula: the area of a polygon with vertices that
have integral coordinates is given by the formula
A = I +
B
2
- 1,
where I is the number of integral points in the interior and B is the number
of integral points on the boundary, including the vertices. We get:

  

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

 

Collections: Mathematics