Note: This post was written hours after the test, but published after the testing window.
This test was an intense battle. It was me vs. me.
This week, I decided to sleep in late on the day of the American Invitational Mathematics Examination (AIME). This was quite a big test for me, as I have utilized the past two months in massive preparation for this contest. During the past two or three weeks, I spent as much as four to six hours per day practicing past problems and reviewing the theory that will likely show up on the test. Although I needed to answer twelve out of fifteen questions to have a chance for the national olympiad due to my low AMC 12 score, I had the better goal of getting the highest index I possibly could. More importantly, I wanted to beat myself and exceed last year’s score of 3.
I woke up at around 10:30 AM today and had a quick breakfast and lunch. My unexcused absence was worth it: I woke up feeling quite refreshed and ready to battle. It also felt good skipping school to take a math contest. I did a past AIME problem and proceeded to get it wrong. I got a tad bit nervous because of it but realized that at least one problem was precisely the get-go of my battle. I was going to leave the emotions and ego behind on that problem and proceed to go into relentless war with myself.
I arrived at my school at one o’clock. Many fellow mathletes were already there. I checked in and hung out with my buddies for the thirty minutes leading up to the test. There was no use studying theory or doing problems at that point because all you can do to optimize your performance is to relax and have fun with your friends. I overheard from my advisor that there was a possibility of having a fire drill right before our scheduled start time. Thankfully, nothing happened, because at 1:30 we were promptly signaled to report to our testing areas.
When the testing signal started, I prayed to God for a good test experience, regardless of my score and whether I made USAMO or not. I also prayed for a clear mind to minimize silly mistakes and to make this a great learning experience. Over my math contest training this past year, I realized that it wasn’t about you versus the other contestants: it was whether you could stand your ground and focus on yourself and your actions.
In tests, even school tests, I don’t immediately grasp the flow of thinking about or solving questions. I hear the flutter of paper, the turning of pages, and the sound of the calloused pencil scraping paper. I hear the bell ring fifteen minutes after the start. However, as I thought harder and got more involved in what exactly I was solving, the background noise slowly faded away and there I was: the problems and myself.
As mentioned above, I had a weak start. I used the “hard-start technique” (first thinking or solving a hard problem) and focused on problem 7 first. It was an algebra optimization problem. I set up the problem using the rectangular form of complex numbers and went back to problem 1. Admittedly, it was daunting. I was given a couple of variable rates and times and had to solve for a certain time when given a rate and time. I knew the concepts used was just distance * time but the wording of the problem tripped me up a couple of times. I re-read and read a third time and a fourth time to make sure I didn’t miss any small details. I wrote down crucial variables and the key system of equations. In the process of solving the problem, I had difficulty solving one of the quadratics formed, so I looked back and checked my work. Making another substitution yielded a nicer equation that enabled me to solve for 
It sucks if you spent your time on finding the right quantities but the wrong answer!
The second problem was a little bit too easy that I doubted myself that there indeed existed real 
Problem 3 was just the game “21” that I played with my friends back in third grade. In this version, each player may subtract one or four from a positive integer. To find the number of such integers less than or equal to 2024, I noticed from playing with small values of 
By this point, I was fully in my flow. I initially did problem 4 wrong because I wasn’t thinking about the problem clearly, but eventually fixed it later on in the test. That wrong 081 turned into the correct 116, saving me a full point. The problem was just conditional probability, except I didn’t compute the denominator correctly.
When I hit problem 5, I drew out a diagram and didn’t have many ideas on what to do. How on Earth do you solve for a length given an obscure concyclic condition?
And that’s when my streak of prayers started.
I knew that there would be many tough problems in the latter half of the test. And even on problem 5, I didn’t find the idea immediately. I started by drawing our center and drawing segments perpendicular to the sides of the rectangle, which must bisect them since they are chords of the bigger circle. I assigned a variable to one of the side lengths and solved for other side lengths. And before I knew it, two applications of Pythagorean on the radius of the circle gave me two equivalent expressions for 
For problem 6, I recognized a similar idea from a problem in an AoPS textbook Intermediate Counting and Probability. However I struggled to figure out the details and got faulty answers. After trying a bit more, I skipped to probelm 10, in which a wild symmedian appears! I laughed at this because the symmedian line was one of the only topics in Olympiad geometry that I was familiar with. Who knew that a Brilliant article hidden in the depths of your mind could save the day? I obliterated the problem immediately with an answer of 113. I drafted ideas for problem 8, which was just finding two different expressions for BC and scaling up the problem.
Seven down, eight more to go.
I took a bathroom break at around the halfway point (before or after I answered seven problems, I did not remember). The proctor checked if I had a phone on me, which was silly because she never made us put our phones on a table as she did last year. En route, I noticed how noisy the outside world was and how everyone seemed to be so relaxed and indifferent. This was high school, not a college-level lab.
I prayed for problem 8 and managed to get an answer. I then proceeded to finish up my plan for problem 7 from the beginning of the test. I eventually got the wrong answer of 180 because I had erroneously forgotten a crucial substitution, thus missing the correct answer of 540 by a factor of 3. This was an extremely disappointing problem to get wrong, as this problem was the easiest one out in the 6-10 range. I spent a huge portion of the remaining time on a #13 number theory but got a wrong answer of 155 (the correct answer was 110) because I had assumed that the minimal number was 
I avoided problem 9 because I didn’t know how to manipulate hyperbolas. Remind me to brush up on conics for the next AIME!
I was stuck in the same position for the last half-hour. I decided to pray one last time just to squeeze out any ideas lurking in my subconscious mind. It turns out that I had much more in me. Despite being stuck on this problem for about two hours, I suddenly came up with a bashy approach of using a combinatorial sum. I bashed for about five minutes and got stuck between my previous answers of 15 choose 4 and 14 choose 4. They were too big for an AIME answer choice between 000 and 999: had the grid been smaller, I would’ve gotten it wrong! With three minutes on the clock, I realized my mistake of assuming 
The timer rang, and the test ended.
Who could’ve known that a matter of three hours could weed out a group of a thousand exceptional kids to just five hundred extraordinary kids?
I compared my answers with my friends and found out that I got an 8. I attempted ten problems but got two wrong.
Problem Distribution: 11111 10101 00000
Score: 8/15
Solve Distribution(right/wrong/blank): 8/2/5
My index for the olympiad was 
