2009 AIME I

The 2009 AIME I answers are posted here on AoPS.

By my standards, I failed with 3 (or 4?) careless mistakes:

  1. Incorrect. Sloppy thinking! 964 is geometric as well, not just 931.
  2. Correct. Silly algebra.
  3. Correct. Silly algebra. :)
  4. Correct. Silly geometry.
  5. Correct. Silly geometry!
  6. Correct. Close call, but caught myself thinking 4^3 = 4^4.
  7. Incorrect. Careless! I got to the end surprisingly quickly, finding that a_{n+1} = log_5{3n+5}, but in my excitement, instead of finding n for which 3n+5 equaled a power of 5, I found n = 5 for which 3n+5 equaled a multiple of 5 instead. ERGH.
  8. Incorrect. Careless. I screwed up simple addition.
  9. Incorrect. Counting problems murder me. Overcounted.
  10. Incorrect. This one wasn’t really a careless mistake. I knew that MVE had to repeat, so I thought about MVEMVEMVEMVEMVE and MMMMMVVVVVEEEEE but never considered something like MMVVEEMMMVVVEEE. eh I was just stupid.
  11. Correct. Easy for a #11.
  12. Unsolved.
  13. Unsolved.
  14. Unsolved.
  15. Unsolved.

for a total of 6 correct.

After crunching through the first 11 problems and checking (shame on me), I had 30 minutes left. Unfortunately, this was when a loud IT guy came in the room and tried to explain to the proctor how to reinstall MS Office on his MacBook; my concentration subsequently fell apart.

So an index of 100.5 (AMC 12A) + 60 = 160.5 this year. Progress from my 8th grade index of 139.5 (AMC 10B) + 70 = 209.5 is something I’d rather not think about anymore. :(

(but I will persevere and receive 138 + 110 = 248 next year!)

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