Tuesday, September 13, 2011
A cute problem
Does there exist an algebraically closed field that is isomorphic to a proper subfield of itself?
Sunday, December 26, 2010
The Best Chinese Food I've Had
Comes from a restaurant called Grace Garden in Odenton, MD. I went there with family this Friday and had a great meal :). Of course, as with most Chinese restaurants, you have to go in a big group so you get lots of really good dishes.
Merry Day-After-Christmas!
Fish Noodles! How do they make fish into noodles? I really want to know.
Golden Shrimp. My cousin took two before I could get the picture :(
Crispy Eggplant: probably one of my favorite dishes that they have
Sichuan Triple Treasure: It's beef tongue, tripe, and intestines I think.
Braised Pork Belly: Always good
Pocket Tofu: It's so soft and has a really good flavor.
Some sort of green vegetable. Someone else can probably actually identify it.
Merry Day-After-Christmas!
Monday, December 6, 2010
Wednesday, November 24, 2010
Too Hard
Whoops, Tim already wrote a blog post with this same name. I'm using it anyway.
I was the problem czar for the Harvard-MIT November Tournament, which happened on Sunday, November 7, 2010. As problem czar, I was responsible for making sure that enough problems got written on time for the contest to run. That in itself was a huge task, made no easier by the relatively small amount of help that the February problem czars gave me. I personally wrote the majority of the test, with help from Travis in some key areas (he wrote many of the geometry problems), and from Jacob in not as key areas (he kept giving me problems about Bayesian inference...).
66 problems later, I get the (somewhat delayed) response from testsolvers: "Too Hard."
What is too hard?
Honestly I am probably too biased to comment, but I don't believe that it's possible for something to be too hard on its own. Being too hard can cause other issues, such as a lack of distinguishing power, but being too easy can also cause that. And I am fully aware of the issues that come from a test that lacks distinguishing power.
So when I see a complaint that something is too hard, what do I think? I feel that it is extremely more likely that some aspect of the undertaker is off rather than that the task is actually too hard. And it seems like others are the opposite -- they would much rather blame the test than the test takers, especially when they are the test taker.
Actually, I do that too. Lots of my blog posts last year were about things that I disagreed with in tests. Was it really the tests that were at fault or was it me? I think it was some of both. I don't think it's deniable that the HMMT calculus test was unable to distinguish between the top 4 competitors (hint: they tied), but at the same time it wasn't like the test gave them absolutely zero opportunity to distinguish themselves (the tie was at 28, not 50).
Regardless, I feel like there is this idea that if lots of people get two or fewer problems then the test is too hard. So, people say, make there be a few problems that everyone will get. But why? Now I've reduced my contest from 10 problems to 7. That doesn't seem useful at all.
I've rarely seen someone look at a test and say ``This is too easy,'' but many people will look at a test and say ``This is too hard.''
I was the problem czar for the Harvard-MIT November Tournament, which happened on Sunday, November 7, 2010. As problem czar, I was responsible for making sure that enough problems got written on time for the contest to run. That in itself was a huge task, made no easier by the relatively small amount of help that the February problem czars gave me. I personally wrote the majority of the test, with help from Travis in some key areas (he wrote many of the geometry problems), and from Jacob in not as key areas (he kept giving me problems about Bayesian inference...).
66 problems later, I get the (somewhat delayed) response from testsolvers: "Too Hard."
What is too hard?
Honestly I am probably too biased to comment, but I don't believe that it's possible for something to be too hard on its own. Being too hard can cause other issues, such as a lack of distinguishing power, but being too easy can also cause that. And I am fully aware of the issues that come from a test that lacks distinguishing power.
So when I see a complaint that something is too hard, what do I think? I feel that it is extremely more likely that some aspect of the undertaker is off rather than that the task is actually too hard. And it seems like others are the opposite -- they would much rather blame the test than the test takers, especially when they are the test taker.
Actually, I do that too. Lots of my blog posts last year were about things that I disagreed with in tests. Was it really the tests that were at fault or was it me? I think it was some of both. I don't think it's deniable that the HMMT calculus test was unable to distinguish between the top 4 competitors (hint: they tied), but at the same time it wasn't like the test gave them absolutely zero opportunity to distinguish themselves (the tie was at 28, not 50).
Regardless, I feel like there is this idea that if lots of people get two or fewer problems then the test is too hard. So, people say, make there be a few problems that everyone will get. But why? Now I've reduced my contest from 10 problems to 7. That doesn't seem useful at all.
I've rarely seen someone look at a test and say ``This is too easy,'' but many people will look at a test and say ``This is too hard.''
Monday, October 11, 2010
Linux iwlagn problems
This isn't really a content-full post, but if any of you are trying to install linux on a new computer and are finding that your internet connection drops after a couple minutes and a bit of traffic, it was a really annoying problem for me that existed for essentially the entire life I've had this computer. I only found the solution a couple days ago.
Right now, the iwlagn driver does not have full support for 802.11n. In fact, having 802.11n enabled will oftentimes screw up your internet connection in a very strange way. You retain your IP address, everything says you're still connected, but no transmission is really happening. You might notice a drop in bitrate from the output of iwconfig, but setting it to be higher again doesn't fix the issue. The issue is 802.11n.
The fix is to initiate the module with the option 11n_disable=1 or 11n_disable50=1. I had to use the latter. I am not sure, but I think it depends on which version of the driver you have (iwl4965 vs iwl5000). So make sure that you are compiling the driver as a module (do not build it into the kernel) and the fix is below.
If you have already booted and want to fix the issue, run the following commands as root
rmmod iwlagn
modprobe iwlagn 11n_disable=1
(or modprobe iwlagn 11n_disable50=1)
If you want the module to be loaded properly on boot, edit the file /etc/modprobe.conf (on gentoo; on other distributions this file might be somewhere else) and append the following line:
options iwlagn 11n_disable=1
(or options iwlagn 11n_disable50=1)
You might also have to use both options. I had to use 11n_disable50 and not 11n_disable. Regardless, one of these two should work and leave you with a perfectly reliable wireless card (without n mode, though).
Hopefully I helped someone with this post! This is a really really difficult bug to google.
Right now, the iwlagn driver does not have full support for 802.11n. In fact, having 802.11n enabled will oftentimes screw up your internet connection in a very strange way. You retain your IP address, everything says you're still connected, but no transmission is really happening. You might notice a drop in bitrate from the output of iwconfig, but setting it to be higher again doesn't fix the issue. The issue is 802.11n.
The fix is to initiate the module with the option 11n_disable=1 or 11n_disable50=1. I had to use the latter. I am not sure, but I think it depends on which version of the driver you have (iwl4965 vs iwl5000). So make sure that you are compiling the driver as a module (do not build it into the kernel) and the fix is below.
If you have already booted and want to fix the issue, run the following commands as root
rmmod iwlagn
modprobe iwlagn 11n_disable=1
(or modprobe iwlagn 11n_disable50=1)
If you want the module to be loaded properly on boot, edit the file /etc/modprobe.conf (on gentoo; on other distributions this file might be somewhere else) and append the following line:
options iwlagn 11n_disable=1
(or options iwlagn 11n_disable50=1)
You might also have to use both options. I had to use 11n_disable50 and not 11n_disable. Regardless, one of these two should work and leave you with a perfectly reliable wireless card (without n mode, though).
Hopefully I helped someone with this post! This is a really really difficult bug to google.
Tuesday, October 5, 2010
Contest Theory
The IOI this year took a radically different approach to contest programming than the IOIs in the past. The Canadian Host Scientific Committee decided that it would be a good idea for the IOI to less favor the teams who have individuals who train very hard on standard algorithmic and data structure problems. I will put off judging whether that was a good or a bad decision until later in this post.
There is one fundamental aspect of writing a contest which is up for major contention and I don't believe that people pay enough attention to it. This is the question that you have to answer before you write a single problem for your test. That question is who should win.
Who should win? It seems like a simple question. The person who is best at math should win a math contest, the person who is best at skiing should win an Olympic medal for skiing. But these answers don't really tell you who should win. If I were to run a contest and I said that the winner would be the person who is best at life, nobody would take me seriously. Why? Because there are a relatively small number of things that would be on this contest. We wouldn't be able to determine the best sports player by just playing football, or just football and soccer, or any other (proper) subset of the sports in the world. And even if we were to play every sport in the world, I'd have to give an arbitrary weighting to each one. How do I compare two people if they have different strengths? It's simply not possible.
This problem arises at a lower level too. Let's look at football. Who is the best football player? I could say let's have a competition where everyone plays football. But this won't work. Maybe one player is a very strong quarterback and another is a very strong wide receiver, but only one of them gets their favored role. Well okay, let's have them pick their positions. We still have an issue. How are we supposed to compare someone's performance as a quarterback to another person's performance as a wide receiver?
Perhaps the answer is to have a quarterback competition, solely to determine who is the best quarterback. That is certainly a possible solution, but sometimes this will make the field too small. Say we object to a spelling competition because there are words from a plethora of sources, which some people will be better at than others. So we use our technique and say okay, we will have a spelling competition consisting of only English words of Sanskrit origin. How many people are specialists of such words? There are probably a few, but not enough to make a competition.
So we need some sort of compromise. We have to accept the fact that there are different specialties within whatever activity for which we hold a competition and that these are in some ways not comparable, but at the same time compare them somehow and determine a winner. It is for this reason that it is not the job of the contest to determine the best, but rather it is the job of the contest to determine the winner.
Of course, if there is a single best competitor, that person should win the competition. If one person is better than everyone else at every position in a football team, he would win a football competition. If your method of determining the winner didn't do that, then you have some problems. But this can be resolved by essentially any performance based scheme that uses positive weights on every event.
But in practically every case, there isn't a single dominating competitor, but rather several top competitors who all do well in different areas. So which one of them should win? It's up to the contest organizers to decide.
And this decision is often very debatable. Perhaps the most prominent example for me personally is the US IMO team selection. There is little argument to be made against the choice to favor those who will bring home the highest IMO scores. The argument stems from the fact that the US team leadership has seemingly decided that the most important subjects to be good at are algebra and geometry, casting aside combinatorics and, to a lesser extent, number theory. It's painful to look at the TST to see three geometry problems, graded in difficulty, so that it is almost certain that geometry skill will matter in team selection, in stark contrast with the single combinatorics problem, difficult enough that only Evan solved it (although I like to think I might have if I hadn't spent nearly all of my time on a geometry problem), clearly not mattering for team selection. The IMO claims to be a contest about all four main subject areas, but the US strategy says loud and clear that this is not the case.
Who is at fault? It's difficult to say. Maybe no one. Maybe everyone. It could be that the lack of combinatorics problems did not stem from a belief that combinatorics does not correlate to IMO score. It could be simply that there was not a sufficient supply of appropriate and interesting problems last year, so the TST was forced to be mostly comprised of the other subjects. But I'm not convinced that this was the case.
So now we return to IOI. The Canadians looked at the IOI and decided that they did not like the choice of winner that was made in the past. They didn't want someone who simply coded problems from online judges for the past year to have an easy road to victory. They wanted someone who could think about a problem which didn't have a standard complete answer and could still perform well.
So they changed the contest.
Gennady still won, of course. IOI might be a case where a dominating force actually exists. Regardless, the IOI change hurt my personal placement, but I can understand where it came from. The Canadians did well to explicate their goals, their means to reach those goals, and why those were their goals in the first place. I agree that the IOI had been reaching a less optimal position by simply escalating the difficulty of algorithmic problems, but I also think that the Canadians went too far in the other direction.
Next time you're involved in running a competition. Ask your group the question, ``Who do we want to win?''
There is one fundamental aspect of writing a contest which is up for major contention and I don't believe that people pay enough attention to it. This is the question that you have to answer before you write a single problem for your test. That question is who should win.
Who should win? It seems like a simple question. The person who is best at math should win a math contest, the person who is best at skiing should win an Olympic medal for skiing. But these answers don't really tell you who should win. If I were to run a contest and I said that the winner would be the person who is best at life, nobody would take me seriously. Why? Because there are a relatively small number of things that would be on this contest. We wouldn't be able to determine the best sports player by just playing football, or just football and soccer, or any other (proper) subset of the sports in the world. And even if we were to play every sport in the world, I'd have to give an arbitrary weighting to each one. How do I compare two people if they have different strengths? It's simply not possible.
This problem arises at a lower level too. Let's look at football. Who is the best football player? I could say let's have a competition where everyone plays football. But this won't work. Maybe one player is a very strong quarterback and another is a very strong wide receiver, but only one of them gets their favored role. Well okay, let's have them pick their positions. We still have an issue. How are we supposed to compare someone's performance as a quarterback to another person's performance as a wide receiver?
Perhaps the answer is to have a quarterback competition, solely to determine who is the best quarterback. That is certainly a possible solution, but sometimes this will make the field too small. Say we object to a spelling competition because there are words from a plethora of sources, which some people will be better at than others. So we use our technique and say okay, we will have a spelling competition consisting of only English words of Sanskrit origin. How many people are specialists of such words? There are probably a few, but not enough to make a competition.
So we need some sort of compromise. We have to accept the fact that there are different specialties within whatever activity for which we hold a competition and that these are in some ways not comparable, but at the same time compare them somehow and determine a winner. It is for this reason that it is not the job of the contest to determine the best, but rather it is the job of the contest to determine the winner.
Of course, if there is a single best competitor, that person should win the competition. If one person is better than everyone else at every position in a football team, he would win a football competition. If your method of determining the winner didn't do that, then you have some problems. But this can be resolved by essentially any performance based scheme that uses positive weights on every event.
But in practically every case, there isn't a single dominating competitor, but rather several top competitors who all do well in different areas. So which one of them should win? It's up to the contest organizers to decide.
And this decision is often very debatable. Perhaps the most prominent example for me personally is the US IMO team selection. There is little argument to be made against the choice to favor those who will bring home the highest IMO scores. The argument stems from the fact that the US team leadership has seemingly decided that the most important subjects to be good at are algebra and geometry, casting aside combinatorics and, to a lesser extent, number theory. It's painful to look at the TST to see three geometry problems, graded in difficulty, so that it is almost certain that geometry skill will matter in team selection, in stark contrast with the single combinatorics problem, difficult enough that only Evan solved it (although I like to think I might have if I hadn't spent nearly all of my time on a geometry problem), clearly not mattering for team selection. The IMO claims to be a contest about all four main subject areas, but the US strategy says loud and clear that this is not the case.
Who is at fault? It's difficult to say. Maybe no one. Maybe everyone. It could be that the lack of combinatorics problems did not stem from a belief that combinatorics does not correlate to IMO score. It could be simply that there was not a sufficient supply of appropriate and interesting problems last year, so the TST was forced to be mostly comprised of the other subjects. But I'm not convinced that this was the case.
So now we return to IOI. The Canadians looked at the IOI and decided that they did not like the choice of winner that was made in the past. They didn't want someone who simply coded problems from online judges for the past year to have an easy road to victory. They wanted someone who could think about a problem which didn't have a standard complete answer and could still perform well.
So they changed the contest.
Gennady still won, of course. IOI might be a case where a dominating force actually exists. Regardless, the IOI change hurt my personal placement, but I can understand where it came from. The Canadians did well to explicate their goals, their means to reach those goals, and why those were their goals in the first place. I agree that the IOI had been reaching a less optimal position by simply escalating the difficulty of algorithmic problems, but I also think that the Canadians went too far in the other direction.
Next time you're involved in running a competition. Ask your group the question, ``Who do we want to win?''
Saturday, July 10, 2010
MOP, ELMO, and thoughts on life
Being a senior changes everything. Entering my fourth and final year as a student at MOP, I had been through everything: red once, blue once, black once (though this year they added a new green, which is the old red, and the new red is the USAJMO winners). Those three years I did everything in the most carefree manner I could. Tests weren't really important. Free time was for relaxing and making sure you don't burn out. Even the TST didn't seem like the biggest thing to worry about. There was always next year.
As a senior I went in to TST with an odd combination of emotions. I really wanted to be on the IMO team once, and this was my last chance, but at the same time I had been hoping to run the ELMO and then I later found out that it was traditional for a senior who did not make the team to run it. ``Okay fine, so I have a consolation prize if I don't make it.''
So I was putting pressure on myself to make the team, but at the same time I was trying to convince myself that it didn't really matter. I looked at the people with whom I was competing and realized that it wasn't a guarantee by any means, but I figured I had a good shot. I thought back to what I was told at Romania: ``Once you've already done well you have the confidence to do well again.'' I thought back to my performance at Romania. Better than I really could have asked for. I tried to be confident.
So I went into the TST room on the first day in an entirely confusing state. Pressured but confident but not really confident and darn blue MOPpers are taking the TST again and hmm I didn't do so well on TST last year and I really didn't spend enough time doing problems this year and also the USAMO didn't do much to get me back in practice and I'd be out of practice anyway and okay well I'm nervous except darn there's no adrenaline in my body. Yeah. It turns out that I do better on contests when I'm nervous and get an adrenaline rush.
TST was a flop. Day one went okay. I missed an inequality that plenty of other people got, but at the same time there weren't that many people ahead of me, and even they were only one problem ahead. Nothing insurmountable.
Day two went almost as badly as last year. You see there's an odd characteristic about geometry problems. You can make a lot of progress and not solve the problem. This is because geometric diagrams have a lot of structure in them. So when there's a geometry problem in the first problem slot, I end up working on it and not finding the solution. A little bit in, I think to myself, ``Hmm, I should probably stop working on this geometry problem and try the next problem which is not geometry.'' Within a minute, I'll find something new about the diagram that seems to be useful for the final angle chase in the solution and I think ``Okay, if this doesn't work I'll stop after five more minutes.'' This happened so many times during day two that I really didn't have a chance to look at the other problems. Yet at the end of the day, it went better than it did the year before. This year I spent 3.5 hours on a geometry problem and finished. Last year I did the same thing but didn't finish. 2010 defeats 2009 1-0.
So I went into day three at a rather large disadvantage. The way it had gone I basically needed all three problems on that final day to make the team. I sat down in Avery 106 at 8:00 for the third day in a row and turned over my paper to see a geometry problem as #7 and a binomial coefficient in a number theory number 9. I hate number theory problems about binomial coefficients (although, to be fair this one wasn't bad. I didn't really have a chance to work on it, though). So I killed number 8, then looked at 7 and didn't really get anywhere. When I turned in my papers I was pretty dejected. ``Ah well, no suspense for me.''
The thing is, nothing is ever completely free of suspense. Even when you're the most confident that you won, or the most sure that you didn't, there's a random worry or hope that keeps bugging you until the actual announcement. For that reason I didn't want to be in the blue room when the team got announced. It had nothing to do with who it would be. It was all that I didn't want to have to sit there while the annoying little voice inside of me would say, ``Maybe he'll ignore the TST score.''
Well, I didn't make the team but I did get to run the ELMO. The ELMO is a math olympiad put together by the returning MOPpers and taken by the first time MOPpers. I failed it massively when I was in red mop XD. The ELMO is always called the ELMO, but what the letters stand for is up to the organizers for that year. This year I decided to put as much of the decision making as possible into the hands of the team leaders, including the name and which shortlist problems would appear.
I had been looking forward to the ELMO for a long time and had written several problems before MOP. As soon as I could I posted a sign informing everyone of the first meeting and, following the tradition started last year, signed it Supreme Grand Ayatollah. I've realized in the last year that I enjoy writing contests a lot more than taking them, so I dived into my role as the head of ELMO with a lot of enthusiasm.
The first order of business when running a contest is to get as many problems as you can. It really doesn't matter whether the problems are extraordinarily good or not, since in a collection of 30 problems you'll probably have 6 that are good or can be made good. So I went about soliciting ELMO problems, ending up with 26 on the final shortlist (after the removal of some problems for various reasons). Of course, there were actually only very few sources for problems.
Well, that's to be expected. One of the things I found out from this endeavor is that writing problems on command generally produces suboptimal results, similar to writing anything else. Inspiration doesn't come when you sit down and say ``Okay, I'm going to write a problem.'' It comes when it wants to, which makes writing large quantities quite difficult. In the end, only 1.5 of my problems made it onto the ELMO, although I think this was a result of almost all of them filling the same niche rather than problem quality.
In the end, here was ELMO Day 1:
and Day 2:
The problems were written by
Overall, I thought the problems were reasonably good, although problem 1 is a rather annoying and not very interesting case bash, and of course I prefer my own combo problems to #3 :-). But anyway, the problems themselves were not too bad this year, but there were lots of traps that were very easy to fall in to (and many people did). So when people left day 1, there were a lot of people saying ``Oh yeah, I solved 1, 2, 3a.'' Very few of them actually got credit for all that. Day 2 was much better in that people basically knew what they solved, but #4 still had a rather large pit that needed to be avoided. Anyway, I'm going to not talk too much about specifics of the problems in case you guys want to try them.
Grading was an interesting, entertaining, and slightly stressful experience, as always.
``Can you tell what this says?''
``How many points is this worth?''
``Do I take off a point for this?''
``Whatever, I'll grade it down and let the team leader coordinate it up.''
This was my second time grading and I've enjoyed it a lot both years, although reading some of the red/green MOPpers' handwriting is pretty annoying. Worst style was not very surprising for me, after seeing the ELMO solutions (don't worry, we did all the grading anonymously. I matched the ID with a name after the grading happened).
After the grading for day 1 was done, we sorted the solutions into 24 folders: one per problem per team and distributed them. Coordination for day 1 would occur during day 2, and the grading for day 2 would be done immediately after with coordination for day 2 happening later that night. Unfortunately, this meant that coordination started at 8 am, so some people missed their coordination time.
Coordination seems like it would be more fun than the grading, but really it's just you arguing for a lower score and the team leader arguing for a higher score. And this almost always involves them pulling some bullshit on you saying that their team member could have done this easily and that they only were missing one tiny step and that the entire problem is trivial so they shouldn't even have to write down anything to get a 7.
The grading and coordination room after everything was complete.
In the end, the scores looked good for our efforts. Nobody had as high of a score as we would have liked (the highest being 33 out of a possible 42 by Thomas Swayze), but the medal cutoffs were approximately what one would see at the IMO, and the total number of points given on each problem were in decreasing order on each day, with 1 and 4 being highest and 3 and 6 being lowest. So although plenty of people (including me to some extent) disliked what the problems ended up being, they gave us a good score distribution.
As ELMO finished, so did MOP. Kazakhstan decided to have a ridiculously early IMO, so we ended MOP nearly a full week earlier than we did last year. This meant, among other things, that we had an extremely tight schedule for getting ELMO entirely graded and coordinated. Day 2 was on Sunday, and the departure day was Wednesday. That's how tight it was. Additionally, because so much of my time was spent on the ELMO, I didn't have time to participate in any of the prepared talent show acts. In practice, that meant that I couldn't dance to Gee. =[ I did, however, get to participate in the MathCounts act again, where I was narrowly defeated by David Yang.
After the talent show were superlatives and then MOP awards. In the superlatives, I procured ``best basher'' pretty easily, having managed to get a 7/0.8 for a dumbass solution to an inequality. In the MOP awards, I got recognized for the only times in all four years of being at MOP. First, I got best style in black, which wasn't too surprising considering I had mostly 0.8s and nothing below 0.7 that counted, while many other people had 0.4s on solutions that got 7 math points. For best style, I got a book of sudoku.
Actually I had another MOP first this year. You see, there are a lot of problems to do on the tests, team contests, mock IMO, and so on. So there is a MOP handbook created with all the problems and all the tests. In order to accomplish this, writeups are assigned to the people who did not solve the problem but had some good ideas on it (and in this year's case, to people who solved the problem in a less than beautiful manner). To assist them in writing up the problem, a consultant, who solved the problem in a very elegant fashion, is assigned. This was the first time I got assigned to be a consultant, and I was very happy when I found out In-Sung's test paper said ``You are writing up this problem. Please consult Brian Hamrick, Supreme Grand Ayatollah, and submit to MOP office by Monday.''
Finally the awards for highest MOP score came. Top four from each group were announced. I was pretty sure that I was in the top 5 in black, but I wasn't quite positive. Anyway, when it was black's turn, fourth was Calvin Deng. My heart sank there, since I was thinking that Calvin was ahead of me, but we were very close. I figured In-Sung was probably third then? In any case, I was wrong. With three fewer math points than Calvin, but a very slightly higher mop score, I came in third place :D. For this, I was awarded play money ``to count, because [I] am good at combinatorics.'' Allen was second and Evan was way ahead in first, although not quite as far ahead as Zhai was his senior year.
Overall, MOP was a pretty satisfying end to my math olympiad career. Although I never got to make the IMO team, I've had in total twelve weeks of great experiences and lots of fun at MOP, and I can definitely say that it has helped me improve a lot. Back when I was in red, I knew so little. I did badly on the red tests that I now find easy, I was horrible at writing proofs (I never got above a 0.7 back then, and this year I never got below a 0.7), and all the rest. I was the lucky one of us three seniors this year; Tim and Travis go nowhere near as satisfying a finish.
I'm very happy with what I got, but you know, I still wish I had IMO as well.
As a senior I went in to TST with an odd combination of emotions. I really wanted to be on the IMO team once, and this was my last chance, but at the same time I had been hoping to run the ELMO and then I later found out that it was traditional for a senior who did not make the team to run it. ``Okay fine, so I have a consolation prize if I don't make it.''
So I was putting pressure on myself to make the team, but at the same time I was trying to convince myself that it didn't really matter. I looked at the people with whom I was competing and realized that it wasn't a guarantee by any means, but I figured I had a good shot. I thought back to what I was told at Romania: ``Once you've already done well you have the confidence to do well again.'' I thought back to my performance at Romania. Better than I really could have asked for. I tried to be confident.
So I went into the TST room on the first day in an entirely confusing state. Pressured but confident but not really confident and darn blue MOPpers are taking the TST again and hmm I didn't do so well on TST last year and I really didn't spend enough time doing problems this year and also the USAMO didn't do much to get me back in practice and I'd be out of practice anyway and okay well I'm nervous except darn there's no adrenaline in my body. Yeah. It turns out that I do better on contests when I'm nervous and get an adrenaline rush.
TST was a flop. Day one went okay. I missed an inequality that plenty of other people got, but at the same time there weren't that many people ahead of me, and even they were only one problem ahead. Nothing insurmountable.
Day two went almost as badly as last year. You see there's an odd characteristic about geometry problems. You can make a lot of progress and not solve the problem. This is because geometric diagrams have a lot of structure in them. So when there's a geometry problem in the first problem slot, I end up working on it and not finding the solution. A little bit in, I think to myself, ``Hmm, I should probably stop working on this geometry problem and try the next problem which is not geometry.'' Within a minute, I'll find something new about the diagram that seems to be useful for the final angle chase in the solution and I think ``Okay, if this doesn't work I'll stop after five more minutes.'' This happened so many times during day two that I really didn't have a chance to look at the other problems. Yet at the end of the day, it went better than it did the year before. This year I spent 3.5 hours on a geometry problem and finished. Last year I did the same thing but didn't finish. 2010 defeats 2009 1-0.
So I went into day three at a rather large disadvantage. The way it had gone I basically needed all three problems on that final day to make the team. I sat down in Avery 106 at 8:00 for the third day in a row and turned over my paper to see a geometry problem as #7 and a binomial coefficient in a number theory number 9. I hate number theory problems about binomial coefficients (although, to be fair this one wasn't bad. I didn't really have a chance to work on it, though). So I killed number 8, then looked at 7 and didn't really get anywhere. When I turned in my papers I was pretty dejected. ``Ah well, no suspense for me.''
The thing is, nothing is ever completely free of suspense. Even when you're the most confident that you won, or the most sure that you didn't, there's a random worry or hope that keeps bugging you until the actual announcement. For that reason I didn't want to be in the blue room when the team got announced. It had nothing to do with who it would be. It was all that I didn't want to have to sit there while the annoying little voice inside of me would say, ``Maybe he'll ignore the TST score.''
Well, I didn't make the team but I did get to run the ELMO. The ELMO is a math olympiad put together by the returning MOPpers and taken by the first time MOPpers. I failed it massively when I was in red mop XD. The ELMO is always called the ELMO, but what the letters stand for is up to the organizers for that year. This year I decided to put as much of the decision making as possible into the hands of the team leaders, including the name and which shortlist problems would appear.
I had been looking forward to the ELMO for a long time and had written several problems before MOP. As soon as I could I posted a sign informing everyone of the first meeting and, following the tradition started last year, signed it Supreme Grand Ayatollah. I've realized in the last year that I enjoy writing contests a lot more than taking them, so I dived into my role as the head of ELMO with a lot of enthusiasm.
The first order of business when running a contest is to get as many problems as you can. It really doesn't matter whether the problems are extraordinarily good or not, since in a collection of 30 problems you'll probably have 6 that are good or can be made good. So I went about soliciting ELMO problems, ending up with 26 on the final shortlist (after the removal of some problems for various reasons). Of course, there were actually only very few sources for problems.
| Name | Problems |
|---|---|
| Brian Hamrick | 8.5 |
| Evan O'Dorney | 4 |
| Carl Lian | 3.5 |
| Others (1 each) | 9 |
Well, that's to be expected. One of the things I found out from this endeavor is that writing problems on command generally produces suboptimal results, similar to writing anything else. Inspiration doesn't come when you sit down and say ``Okay, I'm going to write a problem.'' It comes when it wants to, which makes writing large quantities quite difficult. In the end, only 1.5 of my problems made it onto the ELMO, although I think this was a result of almost all of them filling the same niche rather than problem quality.
In the end, here was ELMO Day 1:
and Day 2:
The problems were written by
- Carl Lian
- Evan O'Dorney
- Mitchell Lee and Benjamin Gunby
- Carl Lian and Brian Hamrick
- Brian Hamrick
- Amol Aggarwal
Overall, I thought the problems were reasonably good, although problem 1 is a rather annoying and not very interesting case bash, and of course I prefer my own combo problems to #3 :-). But anyway, the problems themselves were not too bad this year, but there were lots of traps that were very easy to fall in to (and many people did). So when people left day 1, there were a lot of people saying ``Oh yeah, I solved 1, 2, 3a.'' Very few of them actually got credit for all that. Day 2 was much better in that people basically knew what they solved, but #4 still had a rather large pit that needed to be avoided. Anyway, I'm going to not talk too much about specifics of the problems in case you guys want to try them.
Grading was an interesting, entertaining, and slightly stressful experience, as always.
``Can you tell what this says?''
``How many points is this worth?''
``Do I take off a point for this?''
``Whatever, I'll grade it down and let the team leader coordinate it up.''
This was my second time grading and I've enjoyed it a lot both years, although reading some of the red/green MOPpers' handwriting is pretty annoying. Worst style was not very surprising for me, after seeing the ELMO solutions (don't worry, we did all the grading anonymously. I matched the ID with a name after the grading happened).
After the grading for day 1 was done, we sorted the solutions into 24 folders: one per problem per team and distributed them. Coordination for day 1 would occur during day 2, and the grading for day 2 would be done immediately after with coordination for day 2 happening later that night. Unfortunately, this meant that coordination started at 8 am, so some people missed their coordination time.
Coordination seems like it would be more fun than the grading, but really it's just you arguing for a lower score and the team leader arguing for a higher score. And this almost always involves them pulling some bullshit on you saying that their team member could have done this easily and that they only were missing one tiny step and that the entire problem is trivial so they shouldn't even have to write down anything to get a 7.
The grading and coordination room after everything was complete.In the end, the scores looked good for our efforts. Nobody had as high of a score as we would have liked (the highest being 33 out of a possible 42 by Thomas Swayze), but the medal cutoffs were approximately what one would see at the IMO, and the total number of points given on each problem were in decreasing order on each day, with 1 and 4 being highest and 3 and 6 being lowest. So although plenty of people (including me to some extent) disliked what the problems ended up being, they gave us a good score distribution.
As ELMO finished, so did MOP. Kazakhstan decided to have a ridiculously early IMO, so we ended MOP nearly a full week earlier than we did last year. This meant, among other things, that we had an extremely tight schedule for getting ELMO entirely graded and coordinated. Day 2 was on Sunday, and the departure day was Wednesday. That's how tight it was. Additionally, because so much of my time was spent on the ELMO, I didn't have time to participate in any of the prepared talent show acts. In practice, that meant that I couldn't dance to Gee. =[ I did, however, get to participate in the MathCounts act again, where I was narrowly defeated by David Yang.
After the talent show were superlatives and then MOP awards. In the superlatives, I procured ``best basher'' pretty easily, having managed to get a 7/0.8 for a dumbass solution to an inequality. In the MOP awards, I got recognized for the only times in all four years of being at MOP. First, I got best style in black, which wasn't too surprising considering I had mostly 0.8s and nothing below 0.7 that counted, while many other people had 0.4s on solutions that got 7 math points. For best style, I got a book of sudoku.
Actually I had another MOP first this year. You see, there are a lot of problems to do on the tests, team contests, mock IMO, and so on. So there is a MOP handbook created with all the problems and all the tests. In order to accomplish this, writeups are assigned to the people who did not solve the problem but had some good ideas on it (and in this year's case, to people who solved the problem in a less than beautiful manner). To assist them in writing up the problem, a consultant, who solved the problem in a very elegant fashion, is assigned. This was the first time I got assigned to be a consultant, and I was very happy when I found out In-Sung's test paper said ``You are writing up this problem. Please consult Brian Hamrick, Supreme Grand Ayatollah, and submit to MOP office by Monday.''
Finally the awards for highest MOP score came. Top four from each group were announced. I was pretty sure that I was in the top 5 in black, but I wasn't quite positive. Anyway, when it was black's turn, fourth was Calvin Deng. My heart sank there, since I was thinking that Calvin was ahead of me, but we were very close. I figured In-Sung was probably third then? In any case, I was wrong. With three fewer math points than Calvin, but a very slightly higher mop score, I came in third place :D. For this, I was awarded play money ``to count, because [I] am good at combinatorics.'' Allen was second and Evan was way ahead in first, although not quite as far ahead as Zhai was his senior year.
Overall, MOP was a pretty satisfying end to my math olympiad career. Although I never got to make the IMO team, I've had in total twelve weeks of great experiences and lots of fun at MOP, and I can definitely say that it has helped me improve a lot. Back when I was in red, I knew so little. I did badly on the red tests that I now find easy, I was horrible at writing proofs (I never got above a 0.7 back then, and this year I never got below a 0.7), and all the rest. I was the lucky one of us three seniors this year; Tim and Travis go nowhere near as satisfying a finish.
I'm very happy with what I got, but you know, I still wish I had IMO as well.
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