Was the IMO 2015 Really the Most Difficult in History?
The International Mathematical Olympiad (IMO) held in Hong Kong in 2015 is often cited as one of the most challenging in recent history. This perception arises from a combination of factors including the problem difficulty, historical context, performance statistics, and comparisons with other years. Let's delve into these factors to understand why IMO 2015 is so highly regarded and why opinions on its difficulty vary.
Problem Difficulty
Many participants and coaches noted that the problems presented in the 2015 IMO were particularly tough, characterized by a high level of abstraction and complexity. Some students found it difficult to solve even one problem. For instance, in my personal experience, Problem 1 (P1) was only slightly harder than previous P1s and easier than P1s from 2007 and 2005. Problem 2 (P2) was easier than the average P2, while Problem 3 (P3) and Problem 5 (P5) were considered extremely hard. Problem 4 (P4) was harder for a problem 4, and Problem 6 (P6) was slightly easier than normal.
Day 1 Performance
In the first day of the contest, I quickly finished with P1 and P2. However, I failed to solve P3, which is noted as a very challenging problem. This experience reflects the difficulty reported by many participants.
Day 2 Performance
On the second day, I spent 2 hours on P4 and another 2 hours on P5, leaving only half an hour for P6. Interestingly, P4 and P5 were reported to be very hard, which is quite different from my initial perception. Generally, participants suggested that P2 and P5 were ridiculously hard, and P3 and P6 were considered average.
Historical Context
The difficulty of an IMO can be subjective and varies year by year. While the 2015 problems were significantly more challenging compared to the average IMO, they aren't the only year to have exceptionally difficult problems. For example, 2006 and 2007 are also frequently mentioned as having exceptionally hard problems. However, the consensus among participants and experts is not unanimous. Each year's problems present unique challenges, and these challenges can be influenced by various factors including the preparation of the participants and the nature of the problems themselves.
Performance Statistics
The scores from the 2015 IMO reflected the challenge of the problems. The average score was lower than in many previous years, indicating that even the top competitors found the problems challenging. This drop in average scores led to discussions among the mathematical community about the ranking of the 2015 IMO among the hardest in history. However, the exact ranking is subjective and can vary depending on individual experiences and perspectives.
Comparisons to Other Years
Other years such as 2006 and 2007 are also frequently mentioned as having exceptionally difficult problems. However, the consensus among participants and experts varies. In the case of 2015, some felt that P2 and P5 were the hardest, while P3 and P6 were average. In contrast, 2007 is generally considered to be harder, with high cutoff scores indicating the difficulty level.
Conclusion
While the IMO 2015 is certainly regarded as one of the most difficult, whether it is the absolute most difficult is subjective and can depend on individual experiences and perspectives. Each year's problems present unique challenges, and comparisons can be influenced by various factors including the preparation of the participants and the nature of the problems themselves.