## 24 February 2010

### Harvard-MIT Math Tournament 2010!

This weekend was the XIIIth annual Harvard-MIT Mathematics Tournament! Perhaps the second biggest and second most important competition, all the teams basically just did math the months of January and first half of February to test their skills. Noticing that our team was beast as a whole but lacking individual-wise, Mark-san implemented Operation PICTURE (Pwning Individual Competitions Through Ubiquitously Rigorous Exercise (jeebus, how did i memorize that XD (and yay for the nested parentheses!))) to try to bolster our individual scores. Practice time faded into the past as February 20th rolled around.

This fateful morning, I woke up at 0630. Unable to fall back asleep, I laid in bed until 0715, when my alarm rang. I got dressed in our super special awesome math team apparel (collared t-shirt + sweater) and did some fifteen odd sit-ups and five pushups as preparation. Then I went downstairs, had a bowl of cereal, and left for Harvard.

The car ride was definitely not the smoothest trip. Driven by a PhD, copiloted by another PhD, and directed by a fail GPS, we somehow got lost twice (by lost I mean passed by MIT's Lobby 7 twice :S). Fortunately, after a fifty minute journey (which was twenty minutes too long), I headed into the Science Center to wait for the rest of AAST. Upon entering the building and walking down the hallway, I spotted Brian talking to some of his friends. Unfortunately for him, once I had found a nice spot to stand, I faced the exit to look for the rest of my team.

Not long after I saw Dr. Nevard coming in, with everyone else not far behind. I greeted everyone and made sure everyone was OK (especially Mike Sun and JP). Thirsty, I went to get a drink, but was chased by one of my Exeter friends. It was quite trivial to lose her, and I eventually got a refreshing cup of orange juice and rejoined the team.

By this time everyone was heading off to their testing rooms, and I went with Mike Tan to Calc/Combo + Geo room. The tests weren't so bad, but unfortunately I made some silly mistakes and lost a handful of points. On one of the geometry problems, I did find a really nice solution, but got it wrong because I forgot to multiply by a constant (the \sqrt{2}/2 in the end) -.-

Problem 6: Three unit circles, w_1, w_2, and w_3 in the plane have the property that each circle passes through the centers of the other two. A square S surrounds the three circles in such a way that each of its four sides is tangent to at least one of w_1, w_2 and w_3. Find the side length of the square S.

Solution: Let $P$, $Q$, and $R$ be the centers of $\omega_1$, $\omega_2$, and $\omega_3$, respectively. Notice that the diagonal of $S$ has to pass through one of the centers (let's say $P$) and the intersection of $\omega_2$ and $\omega_3$ only. Now we will compute the length of $AC$. We know that $AC = AP + PS + SC$. $AP = \sqrt{2}$, $PS = PT - ST = \frac{\sqrt{3}}{2} - \frac12$, and $SC = \sqrt2 (\frac{\sqrt2}{2} + 1) = 1 + \sqrt2$. Therefore, the side length of $S = AC\frac{\sqrt2}{2} = \frac{\sqrt2}{2}(\sqrt2 + \frac{\sqrt3 - 1}{2} + 1 + \sqrt2) = \frac{\sqrt2}{2}(2\sqrt2 + \frac{\sqrt3}{2} + \frac12) = 2 + \frac{\sqrt6}{4} + \frac{\sqrt2}{4} = \frac{8 + \sqrt6 + \sqrt2}{4}$. No $\cos 15^o$ crap required! :D

It turned out that I wasn't that much of a failure, as other people on Mu A told me that they also got murdered when we regrouped to go to Sever for the team round.

The team round was equally as rape as the individuals. We only answered five questions (1,2,3,4,6 and wrote a joke for 10). I was somewhat disappointed that I didn't get the only geometry problem (some weird angle chasing stuff), but having realized that it requires some esoteric olympiad geometry knowledge, I didn't feel that bad. After that was over, a hungry Pavel and Sam ran away to somewhere to eat lunch and Mark and I headed to where TJ was eating lunch while the rest of the team decided on sandwiches and pizza.

Jenny graciously waited for us at the entrance and led us to TJ's little hideout.'' She then forced me to eat a pizza, which obviously scared off Mark as he [actually both of us] felt really bad for taking other teams' food. Then Harini came and hung out with us for a while…and it was slightly awkward. XD She dragged us to see some Exeter people, but on my way, I met Jacob Hurwitz and he recognized me XD That was pretty amusing. After Harini left, Jenny dragged us to play Gluck, but I stubbornly refused a countless number of times >D I eventually led them back to where we started and saw some AAST people filtering in, including Sam and John. I started a bridge game with them and Brian. Then a bunch of people gathered around us to watch, but eventually got bored because John played really slowly, as always. Some people wanted to go to minievents, but my parents didn't let them, which was pretty retarded. Taking charge, I dispersed everyone and told them to report to the Guts room by 2:30.

When I got to Science Center B, there was a huuuuuuge crowd waiting outside. I shoved my way through to join Mark and Pavel, who were at the front. The door opened soon after and we all walked or got shoved in, one way or another. Mu A sat in formation, took out scrap paper, and waited for Mark to retrieve the first packet. Occasionally, I reported our performance, but made sure I didn't get too fixated. The eighty minutes flew, and by the end, we emerged victorious by a slim thirteen points!

The eight of us got up and mingled with other people while the HMMT staff were preparing the awards ceremony. Mark, Pavel, and I went to talk with Mu C and the Lehigh people. Then I went back up to sit with the bulk of the team. By this time, the awards preparation was complete and everyone quieted down.

In the individuals, Mark and Sam had honorable mentions in calculus. John got second in combo and placed tenth overall. Brian didn't win any of his tests, which probably was a letdown :( Then was the team round award. Mu A tied with Beijing STFX for second, which warranted a game of rock-paper-scissors. Excited, Mark walked down to the stage'' and put on a small show for all of us :) Although he won, he had to surrender his plaque to China because HMMT does not want to pay shipping to Beijing XD Next was Guts. Happy again, Mark skipped down, retrieved the translucent triangular prism, and put on another little show ^^ He set the trophy down by his feet when he got back, but that turned out not to be the best idea as Alex Zhu almost stabbed himself with it XDD

Finally was the sweepstakes. Everyone was so hyped up for this. The bottom five were pretty obvious; but everyone was super duperly focused on the top five. After 3rd to 5th places were announced, both AAST and TJ were superly anxious beyond belief. Then the announcer opened his mouth and said In second, with one thousand four hundred sixty-six points, which is just three points behind first place, with one thousand four hundred sixty-nine points, we have, Thomas Jefferson A!!!!'' We all cheered as TJ A went up and claimed their frisbees and octagon. At this point, Mark and everyone was getting super jumpy. Then Winston finally called us up and we all ran down! Mark, being a true actor, asked to say a few words while the rest of the team got frisbees. I took center stage and held our nice octagon :D Unfortunately, Mark was unable to contain his exuberance and made a comment that many people took seriously. I don't blame them; the comment was certainly ill-timed, but the way Mark said it indicated that it was completely for jest. Actually I will stop talking about this now because it seems highly redundant when there is lots of coverage already:
http://www.artofproblemsolving.com/Forum/viewtopic.php?t=333745

After that, we all gathered our stuff and headed to the buses and I said goodbye as people boarded.

Dinner was pretty tricky. Brian wanted me to eat dinner with him and Jenny at Harvard Square after they finished with the tour. Unfortunately, their tour finished an hour after I headed to Harvard Square, so I unbored myself by flipping through some magazines in the little newspaper shop. Finally, around 1900, I spot them at a T [bus] stop. We decided to eat at Qdoba (a restaurant like Chipotle) after a bit of indecisiveness.

Upon finishing dinner, we wandered around Harvard Square, first stopping at the Coop only to be deterred by the clerk when she saw Jenny open her can of Milkis. She wanted to drink it after being unable to decide whether to buy a $4.25 slice of chocolate cheesecake, a$2.50 cupcake, or nothing at all out of fear of getting fat XD

Then we wandered to CVS because Jenny wanted to buy some chocolate. She claimed that she was buying them for me, so she could then eat some of it and not be guilty XD We found the chocolate selection and again stood there for about ten minutes before deciding on a bar of Ghirardelli dark chocolate. After she paid for it, we found a bench outside to sit down and eat it. However, I could only stay for ten more minutes because my parents wanted to leave D: At 20:30 I said goodbye to both, joined my parents, and went home.

The Good:
• Teamwork prevails
• Collared t-shirts just in time
• Rape tests even the playing field
• Awesome little afterparty
• Happy ending x2
• Not enough time
• No quiet places relatively near Science Center
• I failed the rape tests
• Pizza for lunch
• Nearly everyone got sick, one way or another
The Ugly:
• Thank you for coming and uhh…losing to us.'' -- Mark Lipa Velednitsky

1. I like how neither me, you, nor Brian bothered to consider a degenerate case in that team problem. :P

2. hey hey hey, i would like to say that i only ate 2 pieces of that chocolate i gave you! >:O!!!! so i did buy it for you. hmph >:[

also *facepalm* i think everyone will have read adam's blog by now

hmm, imma go blog about hmmt sometime ^^

3. btw you owe me chocolate pecan pie...

<33

4. also apparently the actual results is that you guys got 3rd and we got 4th
gg -_-

5. Whoops, looks like you guys didn't win after all :(. Well it makes sense given that everyone massively failed individual. And hey, I still tied for first in calc (and I really should have gotten #2 on combo...but that still wouldn't have been first because of #10)