Well now that both AIMEs are over, I think I’ll take some time to talk about how I felt about this year’s AIME I. I did take the AIME I, having qualified through the AMC 10 with a score of 120. The AIME committee did a good job on balancing the toughness of both AIMEs. To be honest though, I thought this year’s AIME I was much softer than its predecessor. For example, take a look at the 2012 AIME I #6:
6. The complex numbers z and w satisfy z^13 = w, w^11 = z, and the imaginary part of z is sin(mπ/n), for relatively prime positive integers m and n with m < n. Find n. (Source: 2012 AIME I #6) Now I did state that the AIME committee did a good job balancing both AIMEs. However, the problem selection was a totally different issue. Looking at the problem above, most people might shy away due to the elaborate wording and "complex" notation. On the other hand, those experienced with polar coordinates and complex numbers can immediately deduce that they have to simply find solutions to the equation z^142 = 1. In this sense, #6 was an easy problem and a hard problem, only because it was a complex number arithmetic exercise. Simply put, the AIME problem selection committee violated the first rule of problem solving - "A problem is not an exercise." In summary, I thought that the AIME committee could have done a better job in selecting better PROBLEMS rather than EXERCISES. That being said, they did a relatively better job in balancing the difficulty of both AIMEs. However, I hope that future AIMEs will be a little bit more interesting than the ones that were handed out this year.