Students Compete at the 54th Math Olympiad
The brain-pressure is finally over that the results are in as students competing in the 54th International Mathematics Olympiad (IMO) in Colombia head back to their various countries.
The International Mathematical Olympiad is the World Championship Mathematics Competition for High School students and is held annually in a different country. The first event was held in Romania in 1959, with 7 countries participating. It has now expanded to over 100 countries from 5 continents.
Here is a problem from this year’s event:
Problem 2. A configuration of 4027 points in the plane is called Colombian if it consists of 2013 red points and 2014 blue points, and no three of the points of the configuration are collinear. By drawing some lines, the plane is divided into several regions. An arrangement of lines is good for a Colombian configuration if the following two conditions are satisfied:
• no line passes through any point of the configuration;
• no region contains points of both colours.
Find the least value of k such that for any Colombian configuration of 4027 points, there is a good arrangement of k lines.
Perhaps you were at the IMO in Cape Town in 2014?