January 22 – Dr. Dimitar Grantcharov – Interesting AMC and AIME Problems

Metroplex Math Circle will kick off its spring 2011 semester with a presentation by Dr. Dimitar Grantcharov.    Dr. Grantcharov is an assistant professor at UT Arlington and the director of our neighbor, the Mid Cities Math Circle.  Dr. Grantcharov will use problems from last year’s UT Arlington Math Competition to help prepare our students for the upcoming AMC 10, 12 and AIME.  Here are some examples:

Which of the following numbers is a perfect square?
(A) 98!99! (B) 98! 100! (C) 99! 100! (D) 99!101! (E) 101!101!

A square has sides of length 10, and a circle centered at one of its vertices has radius 10. What is the area of the union of the regions enclosed by the square and the circle?

A game is played with tokens according to the following rule. In each round, the player with the most tokens gives one token to each of the other players and also places one token in the discard pile. The game ends when some player runs out of tokens. Players A, B, and C start with 15, 14, and 13 tokens, respectively. How many rounds will there be in the game?