In July of this year, I, along with five other secondary school students from around New Zealand, had the amazing opportunity to travel to Athens, Greece to compete in the 45th International Mathematical Olympiad (IMO) along with over 500 students from 85 countries from around the world. But before the competition began, we, the New Zealand team, spent a week on the beautiful island of Paros, to acclimatise to the heat, relax on the beach,…and soak up some of the Greek lifestyle!
Paros is a wonderful place, the weather was perfect, and the food was great (Souvlaki is surely the best tasting food in existence!). All the houses are white washed and have a little blue line painted around the windows and doors.
All too soon, our week-long holiday was over and it was back to Athens for the beginning of the competition. The IMO is an individual sport, there is no official team score, each student sits two exams, on consecutive days, each four and a half hours long and containing three questions. Each question is worth seven marks, giving a maximum possible total of 42 points.
Despite only fully solving one question, I gained a total mark of 16 which was enough (though only just!) to earn a bronze medal.
After the exams, finally able to relax, we were all taken on excursions to famous landmarks around Athens and further afield. It was wonderful to be able to visit such famous and significant sites as the Acropolis and Areopagus, the temple of Poseidon at Sounio and the ruins of the ancient city of Mycenae; and simply to walk around buildings well over 2000 years old.
Especially impressive was the tomb of Agamemnon, an example of a “beehive tomb” named for its shape. Even today, archaeologists are baffled at how the builders were able to move some of the 120 ton stones comprising its walls to the site.
In all, this was an absolutely amazing trip, and one to be remembered for a lifetime.
Anyway, how about a problem?
We call a positive integer alternating if every two consecutive digits in its decimal representation are of different parity. Find all positive integers n, such that n has a multiple which is alternating.
This was question six (the hardest problem) on the exam this year. Enjoy!