# Treviño attends international math competition

Assistant Professor of Mathematics Enrique Treviño attended the sixth European Girls Mathematical Olympiad as the Deputy Leader of the Mexican team.

Assistant Professor of Mathematics Enrique Treviño attended the sixth European Girls Mathematical Olympiad (EGMO) as the Deputy Leader of the Mexican team (Mexico is invited as a guest country to the competition). The competition took place from April 6 to April 12 in Zurich, Switzerland.

The EGMO started six years ago with the purpose of promoting more women into STEM fields and, more specifically, to get more women to attend the International Mathematical Olympiad (IMO). To participate in the EGMO, contestants must be girls that have not started college yet.

The Mexican team consisted of Ana Paula Jiménez Días, Marcela Cruz Larios, Nuria Sydykova, and Cristina Sotomayor. The leader of the team was Isabel Hubard, a mathematics researcher at the Instituto de Matemáticas at UNAM (Universidad Nacional Autónoma de México). Ana Paula won a silver medal, while Marcela, Nuria and Cristina won bronze medals. This was the first time that all Mexican competitors won a medal at an EGMO.

In November, the best eight girls of the country (Mexico) were selected at the Mexican Mathematical Olympiad, where Professor Treviño was one of the coordinators of the exam. The eight girls then went to intensive 10-day training sessions to Guanajuato (twice) and Mexico City in December, January and March, respectively. Professor Treviño was one of the instructors in the January session in Guanajuato. The team of four was selected after exams in March.

The EGMO has the following structure: there is a two-day exam. On each day, contestants get three problems and have 4 and a half hours to solve them. For example, problem 3 (given on the first day) was:

There are 2017 lines in the plane such that no three of them go through the same point. Turbo the snail sits on a point on exactly one of the lines and starts sliding along the lines in the following fashion: she moves on a given line until she reaches an intersection of two lines. At the intersection, she follows her journey on the other line turning left or right, alternating her choice at each intersection point she reaches. She can only change direction at an intersection point. Can there exist a line segment through which she passes in both directions during her journey?

This edition of the EGMO had 43 countries, with the host, Switzerland, competing with two teams. Therefore there were 44 teams. Mexico ranked 14th among these 44 teams. The first place team was USA, which had an astonishing 148 points of a possible 168. Second place was Ukraine with 126 points (officially, the winner of the title of best European country), and third place was Russia with 125 points. The USA was the only country where every member was awarded a gold medal.

For more information, including the beautiful solution to Problem 3, contact professor Treviño at trevino@lakeforest.edu.