Archive for February, 2012

Uncover A Few

I have a short parity problem on Numberplay (the NYTimes blog) this week!  Thanks to Gary Antonick for the great image and the opportunity to interact with his fantastic readers.I have some variations in mind, to keep making the problem harder once people finish off this easy beginning. I’m curious what variations you can think of to add to the collection!

Feel free to comment here or there or both.

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Our first speaker of the semester, Roberto Bosch Cabrera, has generously provided us with a set of problems and solutions.  The concepts behind these problems should be very helpful to our students preparing for the next set of AMC contests.  In addition, the art of writing excellent articulations like Roberto’s is critical to advancement in mathematics and is applicable to a variety of other fields.

Here are the first two problems and the solutions which you will find in the attached Adobe Acrobat File (pdf).



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February 18, 2012 – Dr. Branislav Kisačanin – “Introduction to Graph Theory”

Graph theory was born when Leonhard Euler solved the Seven Bridges of Koenigsberg problem and has since grown into a mathematical discipline with beautiful theoretical results and with applications in disciplines like theory of dynamic systems, electrical engineering, computer vision, neuroscience, and social networking.
In this lecture we will learn about the fascinating early history of the graph theory, discuss Eulerian and Hamiltonian paths, node and edge coloring, and look at other important properties of graphs, such as planarity. We will even work on several problems like this one from the Sixth IMO (Moscow, 1964):
Each of 17 students talked with every other student. Each pair of students talked about one of three different topics. Prove that there are three students that talked about the same topic among themselves.

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The Preston Trail Chapter MATHCOUNTS competition was held at UT Dallas today.  We would like to congratulate all of the participants but especially the three winners of the Countdown round who are all regular Metroplex Math Circle attendees:

  1. Jeffrey Huang
  2. Vinjai Vale
  3. Michael Ma

Best of luck at the state competition in Austin!

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Bulgarian Olympiad winner, Krassimir Penev will consider a variety of problem-solving techniques and important facts used for solving nonstandard geometric problems. The examples include but are not limited to the Nine Point CircleEuler’s lineCeva’s Theorem and cyclic quadrilaterals.  These mathematical tools could be used for math competitions such as the AMC10,12, AIME, USAMO and Intel talent search.


We will plan to meet right after the MATHCOUNTS Chapter competition.

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