While Metroplex Math Circle is over for the season there is one more Mid Cities Math Circle (MC^2) in Arlington next Tuesday night. Please see more information and contact Dr. Grantcharov through the new site:
Problem sets from previous session are posted on the some. Some examples from the last session are below:
Problem 2. Five married couples gather at a party. As they come in and greet each other, various people exchange handshakes but, of course, people never shake hands with themselves or with their own respective spouses. At the end of the party, one woman goes around asking people how many hands they shook, and she gets nine different answers. How many hands did she herself shake?
Problem 4. A cube 3X3 X 3 is made of cheese and consists of 27 small cubical cheese pieces arranged in the 3 X3 X3 pattern. A mouse is eating the cheese in such a way that it starts at one of the corners and eats smaller pieces one by one. After he finishes one piece, he moves to the adjacent piece (pieces are adjacent if they share a face). Is it possible that the last piece mouse has eaten is the central one?
Problem 5. In how many different ways one can place 3 rooks on the cells of 9X2009 chessboard such that they do not attack each other?