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## One More Mid Cities Math Circle

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:

http://midcitiesmathcircle.wordpress.com/schedule/

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?

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## USAMO Qualifiers

AMC recently announced the students invited to sit for the USA Mathematical Olympiad.  This is a tremendous accomplishment following exemplary performance on the AMC 10 or 12 and a high score on the AIME.  The qualifiers from Texas are:

Every student representing Texas at the USAMO deserves to be very proud.  However, Metroplex Math Circle is particularly proud that one of our most regular attendees is by far the youngest student on the national list.

Michael Ma, as a fourth grader received a perfect score on the AMC 10 and followed it up with a performance on the AIME that is beyond all but the best high school students.  MMC cannot claim the credit for this terrific success (that belongs to Michael and his family) but Michael does exemplify the hard work and talent that Dr. Andreescu seeks to identify and encourage.

Please join us in congratulating Michael on his continued success.

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## April 18 – Last Math Circle

Please join us on April 18 for the last Metroplex Math Circle of the Spring 2009 semester.

Dr. Andreescu himself will present some of his favorite problems and then we will have our traditional end of the year celebration.

Most importantly, we want as many students and parents to attend so that we can discuss the future of the Metroplex Math Circle.

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## Invariants and Knot Theory Recap

Unfortunately, due to state MATHCOUNTS and other activities, many students missed Dr. Razvan Gelca’s excellent talk on Invariants and Knot Theory.  Thankfully Dr. Gelca has made his slides available for these important topics.

You will find several interesting problems and solutions in this first deck:  Razvan Gelca – Invariants1

The second set of slides deals with Knot Theory.  Knot Theory is a good illustration of the importance of pure math and the topics explored through math circles.  For hundreds of years mathematicians explored the various ways that a string or rope could be twisted around itself motivated by little more than intellectual curiosity.  Today, however, we are finding that the principles of Knot Theory are critical to some of the most important applied sciences such as molecular biology.  Razvan Gelca – Knots

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