Recently, I’ve been doing a lot of studying for lots of random crap this winter break. I know it sounds corny, but yeah, I’m just that bored and weird, as I simply admit. As most of you IMSA people might know, February is coming up in just about a month, and since time flies fast, it feels closer than it seems. And guess what that means? A very busy month full of math contests. We mathletes have our fourth NSML meet, hosted by IMSA, the AMC’s (American Mathematics Competitions), Mandelbrot, and ICTM regionals. In case if you don’t know, the AMC contests are a series of math contests that are taken by thousands of high school students in America each year. The series of contests is used to determine the 6-person U.S. team for the IMO (International Mathematics Olympiad) which is a two-day, 6-problem proof-style competition for high school students. Most of the AMC (and IMO) problems are challenging for normal high school students, but with proper rigorous training, it actually becomes a piece of cake if you study well and train your brain to think like a pro mathematician. The AMC series starts with the AMC 10/12, which is for students up to 10th grade and 12th grade, respectively. They each have 25 multiple choice questions (A to E) to be completed in 75 minutes, no calculators permitted. High scoring students (for AMC 10: 120/150 or top 1% of scorers, for AMC 12: 100/150 or top 5% of scorers) get invited to take the AIME (American Invitational Mathematics Examination), which is a more difficult 15-question test (with all answers ranging from 000 to 999 inclusive) to be completed in 3 hours, without a calculator. Then, after that, students take either the USAMO (USA Math Olympiad) or USAJMO (USA Jr Math Olympiad. 10th grade or below), both of which are proof style contests like the IMO. Top scorers on those go to MOP (Math Olympiad Program), a summer seminar to help prepare prospective students for the IMO. Now, since I haven’t made USA(J)MO or MOP before, I won’t go in depth explaining those until I actually do…Oh, and as for ICTM, it’s some really trivial Illinois state math contest sponsored by the IL Council of Teachers of Mathematics. Like NSML, it has grade level individual contests, but also various other events like relay rounds, 2-person team, orals, 8-person team, and stuff like that. It’s also a highly team-based contest too.

Now, in case if anyone else was wondering about NSML, our fourth meet is February 3. The seniors topic is trigonometric equations and identities, which I’m actually pretty happy and nervous about at the same time. Trig is actually one of my favorite subjects, and I’ve been obsessing over it during these past few weeks. (And yeah, doing lots of IMO problems makes it more fun too) However, I found it pretty strange that perfect scores on a topic like this are very rare. O__o

Additionally, Mandelbrot Round #3 is during Intersession week, the first week after break. So yeah….squeezing in lots of prep for that. I’ve gotta just push myself up to the National leaderboard…>.<

Also, in case if anyone was wondering about Olympiad (proof) problems like USAMO/IMO, just google that stuff and you’ll find lots of cool sites for that.

So yeah, I guess that’s all I’ll say for now.

IMSA had 4 perfect freshmen, 2 perfect sophomores, 2 perfect juniors, and 3 perfect seniors (hope I didn’t get any numbers wrong) but yeah, at the very least we got perfect 75′s for the team scores of freshmen and seniors. Wooty frooty! =D

As for the contest, ehhh, there’s not that much to say. The freshman topic was on systems of linear equations and inequalities, which was really trivial because it didn’t even contain inequalities even though it’s supposed to….=0 And the senior contest was perfectly normal for the topic, but still, easy. =)

The candy bar contest was fairly interesting. We got a 16/20 this time, and still won. For some reason, #1 had like 3 disputes before I confirmed the final answer to be right, lol. And some other problems took us a while….like #20, and very strangely, Alina and Adam were like arguing over the answer to Tiebreaker #3…which was kinda funny seeing how they were like almost in an erupted debate.

Other than that, great job IMSA!

Last week, some math team kids and I did the second round of the Mandelbrot contest. In case if you don’t know, Mandelbrot is this nationwide math contest for high school students, that consists of 3 Team Play (proof style) rounds and 5 individual rounds. It’s also written at the local and national level, both of which students get to pick from. Our IMSA coach, Dr. Fogel, runs the Mandelbrot at IMSA. As he often states to kids, he usually has them start on regionals if it’s their first time taking the contest. However, for some reason, he recommended me to do nationals. So I did nationals, and got a 6/14 on Round 1. (FYI, each round contains 7 problems, and the problems are worth the following number of points, in order from #1 to #7: 1, 1, 2, 2, 2, 3, 3. Students get 40 minutes to complete one round, without calculators) I somehow missed #4 on that round due to a stupid counting mistake, and in case if I didn’t mention this before, counting and probability (also known as combinatorics) is one of my weakest math subjects. Actually, it’s kinda unpopular among a lot of math kids because people don’t usually study the theory behind it that much.

For Mandelbrot Round 2, I got a 9, getting everything except for #5 and #6 right. I was kinda surprised at this because I thought #7 was supposed to be the hardest question. Also, it’s worth 3 points. But weirdly, it wasn’t. It was a geometry question. I LOVE GEOMETRY. Like, friggin insanely much, especially for pre-olympiad problems, but for olympiad problems (USAMO/IMO/proof style), I like sticking with algebra that doesn’t involve inequalities. (okay, the reason that I suck at inequalities is that the only ones I know how to use really well are AM-GM and Cauchy-Schwarz, and stuff like Rearrangement, Muirhead, Schur’s, and various others seem a little confuzzling to me). Blech, well I guess the only excuse I can make here is that I don’t study inequalities as much. Now for some reason, I’m starting to hate myself now (well not really, but I’m kinda mad at this) because I didn’t put an answer for #6. I was low on time for this problem. It was so ridiculously easy, a straightforward application of Cauchy-Schwarz. And did I also mention that number theory is on my weak side? Because that cost me two points on #5, which a bunch of people got right. :-/

Ahh, okay, I guess that’s enough discussion on the Mandelbrot for now. Now…NSML #3…Downer’s Grove North…this Thursday! On analytic geometry with conics, complex numbers, and polar coordinates for seniors, and (trivial) systems of linear equations and inequalities for freshmen. Ok, you guys, this is honestly pretty scary but there’s like a 6 (?)-way tie for second place on senior NSML so far, with a score of 44/50. (Yeah, that solely came from that biology genetics conditional probability problem from the previous meet, which everyone except Marc from Naperville North HS and Kate from Naperville Central screwed up on) And as for team IMSA….a lot of tryout results were surprising, in general.

Hmm so I guess that’s all I’ll write for now. Stay tuned for more future entries.

Well, here’s something to think about. Imagine how long it will take for an infinitely hungry person to eat 1337 bags of popcorn, at a constant rate without stopping. Unbelievable? At first, you might attempt at guessing a random number. But can this estimation be done with educated guessing? Well, of course! Think again. Visualize how much popcorn is contained in a standard-sized bag, and estimate the amount of time it’ll take for that person to eat a single bag, then multiply by 1337. And there is your estimate.

You might think at first that these problems are totally pointless and trivial, but they can be good mind benders if you’re extremely bored and need something to think about. These problems are known as Fermi questions. These types of questions require careful critical thinking, some knowledge about how things usually operate in the real world, and generic estimation and mathematical background. At times, Fermi questions can actually be fun if you love to exercise your brain, or if you’re just a type of person curious about large numbers.

….and if you’d like to try some Fermi questions, here are a couple that I’ve thought of off the top of my head:

1. How many times does a person’s heart beat in a lifetime?

2. How many cookies do the people in the United States eat in a year?

3. How many students fail out of MIT in a decade?

4. How many computers will get manufactured in the world within 5 years?

5. How many times will new track and field records in the world be set within a 42-year period?

Enjoy.

The ACSL contest consists of 4 regional rounds, and the top 3 (or 5) people from the top schools from each U.S. and international region get invited to the All-Star Contest in late May 2010. Each round contains a written portion (5 questions in 30 minutes, with no calculators or computers allowed) and a programming portion (1 programming problem to be completed in a 72-hour period). There are two divisions open to IMSA students: intermediate (for beginning high school students) and senior (for more advanced people, usually those who took AP Comp Sci, Object-Oriented Programming, or any kinds of computer science courses before). Each written contest covers a certain group of assigned topics, while the All Star is harder (yet same format) and could cover any topic. For some reason, yesterday, with the first ACSL contest of the 2009-10 season, I got a 4/5 on the intermediate (stupid mistake on a computational recursion problem) and a 5/5 on the senior test. It kinda sucks to make stupid mistakes, mostly because there might be ties, also a lot of IMSA people are beastly. This first round’s topics were just recursion, computer number systems, and LISP programming (an old computer programming language developed by MIT professors in the mid-20th century), which are quite easy to understand once you know your basics. Also, a lot of it is very mathematical, so if you’re a math person like me, you’ll have fun with this stuff.

For yesterday’s contest, I chose to waver my participation in the programming portion and perhaps wait till the next round or so. I haven’t really had much time to learn programming much, since our contest advisor only introduced it 2 weeks ago. She suggested me to learn Visual BASIC, which seems like a straightforward program for beginners, but my parents (who are computer engineers) think I should do Java or C/C++ programming, since they’re more practical and powerful. But I can’t take THAT large of a step just yet. I have to admit, I’m a complete newbie at computer programming, so I have to first get used to the style, language, and what it’s like to actually do it.

During the past few days, my mom tried to get me exposed to what it’s like typing in Java. The commands are pretty easy to input, however, the programs seemed intimidatingly hard to create. She gave me some basic programs that she made in the past, and I tried out a couple of experiments with them. They were actually pretty cool. Some of those programs were:

Fibo: if you type in java Fibo n, it generates the nth Fibonacci number.

Square: if you type in java Square n, it generates a square of n*n dots.

Echo: if you type in java Echo *insert message here*, it returns you your original message, *insert message here*.

All it takes is first writing the program and then saving it to your computer, then use Java, jc (compile) it to get it running, and then just run it. Simple as that (for using it), but the writing process of the programs seemed complicated to me. For some reason, our ACSL advisor thought Visual BASIC is easier to learn than Java, but my mom unfortunately hasn’t learned it before. Maybe I have to self-teach myself BASIC, but oh well. Gotta get it on, get in movin’, get in going.

Well, as expected, team IMSA came in first place at the 5-school site at Stevenson last night, and of course, first place in the whole league. The freshmen got second, sophomores first, juniors first (with tie with Vernon Hills High) and seniors second. Apparently the tests this time seemed pretty brutal. They featured counting and probability, which most kids think is the hardest topic. Fortunately though, I was the only perfect (fre)shmen at the site, and one of only 2 perfect (fre)shmen overall in the entire league (The other freshie was from Naperville). But I misread the last question (which almost everyone got wrong) on the senior test and ended up with a 19/25 on seniors, which was still the highest IMSA senior score, yet I wished I could stop stupidly misreading problems….=/ Somehow, nobody at IMSA nor the site got a perfect senior score, but one boy from Naperville North and one girl from Naperville Central were the only ones in the entire league to get perfect senior. (And they’re actual seniors, not younger versions of them ) Vlad, our oralist, came in first in the entire league, which was very awesome. (By the way, he’s definitely a beast) This meet’s oralist topic was on parametric equations and their applications. And to make the pwnageness of IMSA to its greatest boost, we WON THE CANDY BAR CONTEST!!! WOOT! The candy bar contest was a 20 question contest where the whole school team worked together to finish the 20 problems in 20 minutes. (It also included 3 tiebreaker questions) I thought the candy bar contest had much more interesting problems this time, which was nice, and I somehow got a chance to solve more problems and at least be a more active contributor to the team. Tiebreaker T1, which was a geometry question that asked to find the area of a triangle in 3-D space, was a little brutal at first, but apparently some geometry whiz from our team got a hold of that problem. (I don’t know if our team got it right, but still, at least we were confident on every question ) As expected, the perfect scorers (me, Derek, Adam, Rose, Peter, and Madhav) got to choose candy bars first. Fortunately, I got a 3 Musketeers bar. =) I also forgot to mention, we got some boxed dinners that were better than Sodexho dinners (which suck!), with veggie/turkey/ham/salami sandwiches, bottled water, two cookies (chocolate chip, sugar, M&M), an apple, and a bag of Lays potato chips.

And if you guys really wanna try the last problem of the senior test, here it is:

A certain trait is simple dominant, which means that everybody receives one gene from each parent relevant to the trait, and they have the trait if either one or both of those genes is for the dominant trait. They only do not get the trait if they get two recessive genes, one from each parent. For a particular simple dominant trait, exactly half of the population has the dominant trait and half has the recessive trait. If two people with the dominant trait have a child, what is the probability that the child with have the dominant trait? Give an exact answer.

(By the way, most kids got a bunch of random weird answers for this problem. I put 15/16, and the actual answer was supposed to be 2*sqrt(2)-2)

Have fun solving this, and cheers to all.

So, as most IMSA people might know (as well as some GBN math teamers), one of the major math contests the IMSA Math Team does is the NSML (North Suburban Math League) contest, which is a local contest for high school students around the North Suburban Chicago area. A conference of 50something schools is competing this year in 4 individual (regular 5-school meets) and 1 final conference meet at Evanston (which is by invitation only, with all 55 schools going to Evanston). Each individual school has its own meet site for the 4 regular meets. The previous meet IMSA was in happened on September 30, 2009, at Naperville North High School. In addition to Naperville North, IMSA’s rivals there were Stevenson, GBN, and Naperville Central. For like the first time in a long history of IMSA participation, the whole team got perfect scores for all four grade levels–frosh, soph, junior, and senior! (And yes, we are getting awarded with a special pizza party)

The competition is structured with 5 questions to be completed in a 30-minute time limit. Calculators are either permitted or non-permitted, depending on the topic covered. Each individual meet/grade level covers a different topic. School teams also select 1 person to compete in the orals competition, where he/she gets a certain amount of time to prepare and present an oral topic. Last time, an IMSA senior represented the school and did a presentation on Taxicab Geometry, which to him, seemed like a pretty interesting topic, not as hard as it sounds.

Last meet, the frosh and soph topic was sets, logic, and Venn diagrams. The junior topic was Coordinate Geometry, and the senior topic was Complex Numbers. I competed in the frosh (because I’m an IMSA shmen) and senior (just because I chose to) contests, both of which I was a contestant, which at the beginning of the year,  I found rather surprising because I was a little intimidated by the seniors at first, no offense to anyone  in particualar. (Meh, well, at least I got over the anxiety) I got perfect scores (25) in both, and got 2 yellow NSML ribbons for them. As a contestant of the first place IMSA team for both grade levels, I ended up getting 2 blue NSML ribbons. (Man, wish there were better, cooler awards…)

This time, the competition is…..*holding suspense*…..TOMORROW! Gosh, why am I still not in bed? (Surprisingly enough, sleep deprivation hasn’t really affected my math performance dramatically, but still…O.o) Again, I’m reppin’ on the frosh and senior teams, as a contestant for both. However, this time, the school is only sending a maximum of 10 people per grade level. It used to be 15 per grade level, but now NSML only accepts 5 alternates per school instead of 10. Gosh. Darn. It. That means some of my besties (and some didn’t try out :’() don’t get to go. Fortunately enough, Rose is a contestant on both the sophomore and junior teams. I’m happy for her. (Oh, and as a side note, she’s doing Math Prize for Girls in New York this Saturday) Unfortunately though, this meet’s topic is Probability, for all four grade levels, except that sophomores are only doing GEOMETRIC probability. And probability=fail, for me. Ok…so I really have to do well….I want those perfects again….And IMSA’s gotta win again….and kick Stevenson’s butt in the candy bar contest! Last meet, Stevenson beat IMSA in the candy bar contest. By the way, the candy bar contest is a side NSML event that involves the whole school (all four grade levels) working together in one classroom to solve 20 problems in a very tight time limit. And obviously, the winner gets, uh, candy. Duhh.

Ok guys, I guess that’s all I’ve gotta say for now, since I’d better be off to bed. Good night, keep reading this blog, be happy, and enjoy your time here and whatsoever.

I mainly got inspired to learn pencil spinning by the people in my math class. Most of them do math team, and actually are fairly devoted to math. A bunch of Asian boys there actually know how to pencil spin. I’ve seen these two guys who were able to spin their pencils like beasts. I mean, like, they take a pencil, grip it with the index finger, middle finger, and thumb, and calmly spin it without any brute force at all. Once you actually get the hang of it, it’ll look cool to you. Like, REALLY COOL. Okay, so would you like to really learn how to spin a pencil? Here are my methods, described in just 3 simple steps:

1. If you’re a beginner, start out with a blunt wooden pencil. Thinner ones would help you get adjusted for normal spinning. Practice using an unsharpened pencil, so that if you make a mistake, you don’t accidentally stab someone in the eye.

2. Hold the pencil in your dominant hand. Grip it around halfway between one end and the middle. You don’t want to hold it directly in the middle, nor on the end. You want to have weight balance, so that when the pencil completes a full revolution around your thumb, the weight shifts to the other end, allowing you to catch and re-grip the pencil. Be sure to only use three fingers to grip the pencil: your middle finger, index finger, and thumb. Grip the pencil only with the tips of your fingers. Do not grasp it too tightly or hold it as in you would normally write with the pencil.

3. Gently use your index finger and push the pencil around your thumb. (Sorry if I can’t explain this well. Credits for my learned method goes to a YouTube video which I’m posting for this entry.) Make sure to keep your hand relaxed. Do not fidgit with your hand. KEEP IT RELAXED, or you might end up with a higher risk of dropping the pencil. With practice, you should eventually be able to spin the pencil once around your thumb, and catch it between your fingers.

Once you become a master, feel free to try other tricks, such as the up and back trick and the continuous spin. Or, if you’d like a bigger challenge, try spinning a mechanical pencil, a pen, a soft-grip pencil or pen, or even so (if you’re really crazy beast)….A BANANA!!!! (By the way, check out the video here: http://www.youtube.com/watch?v=GdVVt_jXJvM)

Below is a picture of the proper pencil spin grip. Notice how I’m keeping my hand relaxed, gripping the heavier end (if you’re using a pencil/pen with a grip), with only my middle finger, index finger, and thumb.

Hope you guys enjoyed this entry.

OK, so let’s begin. I’m currently a 15-year-old sophomore in high school. I was born in Naperville in September (lived there not for long!), and lived in metropolitan Chicago for approximately 5 years. (Dang, I wish my parents let me stay in Naperville) Then I moved to Northbrook, where my family still resides now. I lived my entire elementary and middle school life in Northbrook, where I attended Hickory Point School from kindergarten to third grade, Shabonee School during 4th and 5th grade, and Wood Oaks Junior High School from 6th to 8th grade.

For some reason, I just didn’t like my life in District 27. (No offense intended to anyone who liked it there) When I was young, I didn’t feel the importance of school. At all. The school was not so good, and I didn’t really feel motivated. That’s one reminiscence that makes me jealous of hard-working Napervillians So I didn’t take it too seriously. Then my parents got mad at me when I asian-failed the second grade standardized tests, especially the math portion. (Yes, I’m serious. Before second grade, I morbidly sucked at math) That was my cue to actually study hard to live up to my parents’ expectations. I eventually rose to the top, and started Algebra I near the end of third grade.

I was already ready to conquer anything. By developing my habits, my personality got transformed entirely, to the nerdy scope at around 6th grade. Wood Oaks placed me in Honors Pre-Algebra in 6th grade, the highest math class students were allowed to take. I got sick of that class. It was so boring, and I learned nothing. To avoid wasting my time, I requested that the teachers move me up to a higher math class, so I ended up in 8th grade Algebra I during my 6th grade year. That was also the year when I started to become serious about competition math, and various kinds of strange stuff. I first did MathCounts, the premier middle school math competition in America. At the regional level, I took 6th for the North Suburban region, out of around 200 students who competed.

My parents then realized that I was like a single place away from reaching state. I wasn’t so aware of this at that time, but now as I am knowing this, it somehow embarrasses me. =( So I decided to actually work harder. In 7th grade, I actually knew what it’s like to truly study for a math contest. That means working on NONTRIVIAL PROBLEMS. Yep. NONTRIVIAL PROBLEMS. And high school Geometry didn’t actually count. (Yes, that meant I was actually bored in Geometry when I was in 7th grade) So, to avoid wasting time, I continued self-studying. That eventually led to me making National MathCounts in 8th grade. (where I was a point away from qualifying to the oral finals) 8th grade was also a year for my newly found transition to high school level math contests. That year, I did the USAMTS (USA Mathematical Talent Search), the AMC 10 (American Mathematics Contest 10, students up to 10th grade could take), and the AIME (American Invitational Mathematics Examination). Sadly, I didn’t make USAMO (USA Math Olympiad), a proof-style contest, which I was desperately aiming for that year. Hopefully, this year should be better for me.

All that aforementioned stuff was important to me, but the kids at Wood Oaks didn’t really think so. In middle school, I was not very popular. To be honest, I guess I’m blaming that on the lack of math motivation in Northbrook. (Yes, that includes the whole city!) Wood Oaks, along with Field Middle School, are the only two schools that do MathCounts. I also realized that the local high school, Glenbrook North, seems to be very heavy on sports (especially basketball and football) and not very focused on math and science. AND THAT IS UTTERLY FAIL.

To avoid that trouble, my parents decided that I should apply to IMSA (IL Math and Science Academy), so that I wouldn’t have to attend stinking GBN. So I applied, and got accepted during my 8th grade year. Fortunately, I entered IMSA as a shmen (sophomore who skips ninth grade) so I never have to attend GBN for the rest of my life. Yayness!

Right now, as an IMSA student, I really liked it so far. It becomes very clear to me that if I had a choice, I might not want to ever come back to Northbrook (Again, no offense to people living there), because IMSA people are just so cool, entertaining, funny, smart, social, open, and motivated. It didn’t take me that long to adjust to life there. I’m pretty well-adapted with living and learning with the best high schoolers from Illinois. (As well as going to class with kids at least 1 school year older than I am) Oh, and did I forgot to mention that I live in 1503A with Wendy as my roommate? Well, both her, my wingmates, and hallmates are pretty cool. I also have to mention that my MathCounts friend Rose is rather entertaining.

IMSA’s clubs seem to also get me interested in a bunch of different things. I’m currently in Math Team, ACSL club (computer programming), and Robotics (for the CAD–computer programming branch). So far, not really much has happened in them, but they seem cool. For Math Team, we have finished our first NSML (North Suburban Math League) contest on September 30. IMSA pwned, obviously, with first place in all four grade levels. Plus, our individual scores were all perfect marks for the team. Yayness!

So I guess that’s all I’ll say about myself.

Now for the blog, due to my amazingly high range of brain motivation, I plan to do lots of things for this blog. (Aren’t I getting obssessed now?) Some stuff I planned to include in this blog are: (but not limited to) math problems to help some IMSA people, self-written math articles, original/own problems, funny videos that I find (which mention stuff like math, Rubik’s cubes, computer stuff, crazy stuff, fails, etc.), and various other things that I find interesting for this blog.

Hmm, I guess I should end this entry now. I guess this is like the longest thing I’ve ever typed in an online post/blog. Feel free to comment on anything, and, as always, enjoy your time on my blog.

But anyways, hello and welcome to my blog.

I’m primarily going to be using this blog to track things that float around my mind. And yep, as you might have correctly guessed, I am a deep thinker. My primary interests are math, Rubik’s cubes, computers, and anything that sounds interesting and fun. Feel free to view this in your leisure time. On certain occasions, I might post some things that I find interesting and mentally challenging, ranging from math problems to pictures/videos and other nerdy crap. Yeah…so you probably get the point by now.

Oh…and one more thing: I’ve set this blog to private. That means you must be authorized by me, and me only, to be given permission to view this blog. Guests, please do not share the link to my blog with others without my permission first. This way, I can avoid getting my blog stalked.

Thank you for taking the time to read this entry, and enjoy this blog.