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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. What is
(6 -

6)6
?
(here, x denotes the ceiling function, i.e. the smallest integer n with n x).
(A) 0 (B) (C) 6 (D)
2004 (E) 56
Solution. This is just a cool fact for a warm-up. See
http://mathpuzzle.com/2004.txt and the sequence A091146 at the Encyclo-
pedia of Integer Sequences http://www.research.att.com/~njas/sequences/
for more information.
Problem 2. Find

  

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

 

Collections: Mathematics