This article is published in the June/July 2012 issue of MAA FOCUS.
The 2012 Romanian Masters in Mathematics was held in Bucharest, Romania, February 29−March 5. The U.S. team comprised six high school students, selected by the MAA’s American Mathematics Competitions program to participate in this invitational Olympiad-style problem-solving contest:
Joshua Brakensiek, Phoenix, Arizona (homeschooled)
Mark Sellke, West Lafayette, Indiana (William Henry Harrison High School)
Thomas Swayze, San Diego, California (Canyon Crest Academy)
James Tao, Hoffman Estates, Illinois (Fremd High School)
Victor Wang, St. Louis, Missouri (Ladue Horton Watkins High)
Dai Yang, Irvine, California (Phillips Exeter Academy)
Razvan Gelca of Texas Tech University in Lubbock served as team leader, with Zuming Feng of Phillips Exeter Academy as deputy leader.
Victor Wang won a gold medal, and the other five team members each won a bronze medal. Feng says, “Our students did an excellent job—getting medals in RMM is a very difficult job because the contestant pool is very small and of very high quality.”
Romania and China tied for first place this year, determined by the sum of the three highest scores from each team. Russia placed second; the USA team placed third. All individual scores and team placements are at rmm.lbi.ro.
This is the fourth year that the MAA has sponsored a team at the RMM. Team members were selected on the basis of scores in the 2011 AMC competitions, the USA Mathematical Olympiad, and performance at the previous summer’s Mathematical Olympiad Summer Program.
Getting to Romania was tough this year, both competitively and literally. Because a European air-traffic-controller work slowdown canceled flights, the team spent almost two hours at the airline ticket counter changing itineraries. The team arrived a little late but apparently no worse for wear.
Although team leader Gelca has Romanian as his first language, which helps with travel, language differences turned out not to be a complete obstacle in other ways: In a visit to the Grigore Antipa Museum of Natural History, the boys saw exhibits with various kinds of animals, including “some huge, scary-looking insects,” relates Mark Sellke. One room had a computer test about human anatomy. The team was ready for a challenge, so they took the 20-question biology test—in Romanian. They worked together to identify cognates, both from English and from their French or Spanish classes. They finished with a score of 15.
As for grading competition papers from multiple countries, Feng notes that following clear mathematical reasoning in every language is feasible. No matter the written language, essential mathematical ideas shine through.
Here’s a problem that was solved completely by all six USA team members; it appeared as problem 4 on the competition:
“Prove that there are infinitely many positive integers n such that 22^n+1+ 1 is divisible by n but 2n + 1 is not.”
Try it for yourself.
You can see all the problems from the competition along with the others contestants’ names and their scores at rmm.lbi.ro.
Congratulations to the team and leaders.
Steven R. Dunbar is director of the American Mathematics Competitions program.
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