Solving the 2006 IMO Problems: Day 2
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- Опубліковано 19 тра 2008
- The 2006 US IMO team members describe the steps they took to solve problems 4-6 of the International Mathematical Olympiad.
Hard Problems is a feature documentary about the extraordinarily gifted students who represented the United States in 2006 at the world's toughest math competition-the International Mathematical Olympiad (IMO).
hardproblemsmovie.com
maa.org
All I learned from this is that I need to subtract one form both sides.
2:03
Goes to show that no matter what heights you reach,that negative will always be ignored somehow
I used to know Alex Zhai back in elementary school. We lived in the same apartment complex in Pittsburgh, PA and he was my good friend back then. It's good to know he's come a LONG way. He was practically better than me in EVERYTHING and i kinda looked up to him.
what I have learned from this is I need long hair. Thank you.
I noticed that too 🤣
Alex Zhai sounds super humble. Glad he won gold the next year.
Wow!! Didn't understand a word but loved listening to these kids anyway.
I also loved how frank/modest they were about their own abilities and generous about others
Arnav tripathi the Won gold
Zeb Brady won gold
Alex zhai won silver
Zach Abel won silver
Amazing performance by all
Kudos👌
Skippy Cavanaugh Zeb Brady is currently a grad student at Stanford.
Alex Zhai did not win a gold medal in 2006, however he obtained a perfect score and, thus, a gold medal in 2007.
don't forget Ryan Ko and Yi sun also both got silver medals in 2006
man i wish i took an interest in math at a younger age
It’s never late, man.
find a math book and teach yourself (or find a teacher) :D believe it or not math isn't just for high school geniuses or even college graduates. go love life and explore your interests!
@@abdesakib4424 Yes it is. Once you need to get a job and can't find time for yourself to learn new things effectively during the day, it becomes too late.
People find time for UA-cam or scrolling Instagram after the day at work.
They could explore the math during that time. It’s never too late.
They got medals in the international math olympiad. In essense, they are some of the best in the world for their age. I'm sure they'd be able to get A's in a standardized test.
I suck at math but I would love to be tutored by any of these guys. It seems with their intuitive insight they could teach me.
@bodwisa Hmm, youtube format seems to have gone downhill since google took over. My second post appears before the first one instead of after. My apologies to those who may be reading.
Where can we download the entire documentary in its entirety? Looks very interesting and I'd like to see more problems from the IMO.
no
If you want to see more problems, then you can go to their website and you will find all the problems ever given to IMO contestants in history.
@openuniverse2003 Wow.. if that's you're real concern, then you're way off. Career wise, they will end up as university lecturers, renowned experts in their field or fields medal winners (as Tao from the video did). Or else they will be researchers at a university, technology company or a think-tank, or they may work in government research / intel. If not, they will secure high profile banking jobs, modelling all of the mathematics behind such systems etc. Mathematics can take you anywhere.
24 / 4 + 3 = 9
1 fish + 2 chips + 3 salt = 6 a nice meal.
...pick any number, real or complex. Call it A. Add 1, giving B. Multiply, giving C. Finally, add 1 to C to yield D. Show that A^2 + B^2 + C^2 always = D^2. (A fun, easy problem!)
2:24 kid looks like that kid from Clint Eastwood's Gran Torino 🤣🤣😂
They became like this through hard work and determination
Lol.. in part. You need to be born with the right brain.
@thedipmeister how do you train tests? i only ask because id like to aswell. ive always been pretty good at math but ive had to study on my own independently since the schools i was at didnt offer higher math programs. any books or anything to suggest?
Yesss make it a popular sport get people interested!
The indian dude is Arnav Tripathy, and he has won the Putnam competition 3 times, he should win it again this december, which would make him one of very few 4-time winners.
First problem is the only IMO problem whose solution I could understand. :-) :-)
aren't they high school students?
is there any imo you tube channel?
8:15 Bad Pokemon and turn it into a good pokemon. I did understand that problem!
My former supervisor was a gold medal in IPhO and silver medal in IMO. I am so proud of him.
These guys aren't learning from common core that's for sure
That's because common core is absolutely useless, and you will never get anywhere in life with it. It teaches no problem solving skills, where competitions make problems to test your problem solving skills.
I am 41 years old and I have just taken the under 8 year old's Junior Mathematics Challenge, 2007.
I got about half the questions right, if that.
Good knows how clever the International Maths Olympiad contenders are?!
kuz whatever system you propose would turn the average kid into those super geniuses
So there is no way I could find this documentary streaming online?
Man , I so wanted to go the camps but sadly was rejected in the camps
..
Alex is at Harvard too and Zeb is at Caltech.
Why am I watching this I struggle with my 2x table 🤔
@openuniverse2003 It sounds incredibly sad when the poor bicker about those above them...
Substituting 2^x=Z, and arranging it will give a hyperbola, then you can make some solutions for this equation
when you say that you know that sort of guys,what kind of experience are you refering to?
@blancmange45
no, it does not stream anywhere
MERCI POUR LA SOLUTION MAIS J AI PAS COMPRIS POURQUOI Y-1 EST DIVISIBLE PAR 2 EXP X-1 ET NON PAR EXP X
how long do they have to solve these problems?
i like the Facter IT
@thedipmeister Right on...like Ray Charles said in the movie....''I'm thinking dollars man."
Terence Tao is the best living mathematician in the world.
His Brain at 3000 Hz, Mouth at 60 Hz, A Genius ,,ff
@angela1894 Wrong. Zhai is the best here based on his USAMO and qualification results. He had a disappointing IMO but was only a sophomore here. He would win golds his next two years and even produced a perfect paper as a senior.
Two students and the coach named with "Z"
@blancmange45
Order the DVD from the Mathematical Association of America.
In the solution to the first problem, it states that since both y-1 and y+1 are even, and exactly one of them is divisible by 4, then x>_3. Could someone explain why? I don't seem to understand.
Aoden Teo
thats because if we look at congruence modulo 4, if both are even, then one must have remainder 0 and the other 2 necessarily, that means exatcly one is divisible by 4
flashdrive Thanks
A very fun and logical way to think this explanation is that , if there are two consecutive even integers which are greater than 4 , then one of them will be always divisible by 4 . And here , Since x>=3 works for the expression , so 2 raised to the power x will be greater than 4 and consequently , (y-1) and (y+1) are greater than 4 . That's why one of them is divisible by 4.
6:09 of a convex polynomial
All my COACHING toppers make into this.
damn, it's a little discouraging seeing young people doing problems this complicated, but it is a competition, after all.
@Ameya Chandra Yep. Agreed
@thedipmeister How old are you?
I'm curious, was he just good at math, or good at everything else ??
We would love the opportunity to sponsor 1 or more US IMO team members, all s/he need do is wear an Armis t-shirt, or cap during team interactions.
A little bit of both.
Dude, I knew Alex Zhai
Johnathan Maximillian ,how?
there is no such thing as "extraordinarily gifted students" its hard work.
nextblain There is
Anyone going to take the Canadian Open Mathematics Challenge next year.
i can do #4, after they explained it though lol.
Long time ago bro, i moved on.
2+2 is 4, minus 3 is 1 quick maths
But how you could do that if you even can't solve some hard problems. doing so is the way to do proofs but usually it's less puzzling than dealing whit proofs. and some day you gonna do well. as Perelman the one who solved the Poincaré conjecture once he was a IMO competitor dealing whit that kind of problems (in 1982) after he become theorems proof dealer. but you could be one without being one of IMO competitors. Math is beautiful isn't it?
I believe these kids who do well on these math olympiads might be the smartest people on earth. I know IQ tests are more than just math, but I am sure that anyone that can do well on these math olympiads will have no problems acing an IQ test. All these kids in this video have at least an IQ of 180.
english pls?
i go to a school with 2/3 foreign exchange students, and i a lot of them are chinese, taiwanese, japanese. I can say that they are not really smarter, but just more well educated. Math is practically forced down there throat in Asia. There are a lot of brighter students I know who would of dont exceptionally well with a more rigorous education like those offered in Asia.
Just found out that Alex Zhai went to my school ^_^
really? Which one?
can anyone become like this , or these people just born like this?
he's got indian parents. this comes on TV every once in a while. i've recorded it.
I got the last one, with some help.
Arnav Tripathy (the indian dude) was easily the smartest of the bunch
Quick math
Your spelt your name wrong....
HOW OLD ARE THEY?? PLEASE
All highschool age
you basically, have to be a prodigy at mathematics to to be in that team (USA IMO TEAM)
No
Says a guy who uploads gameplay of flash games.
anyone know where to watch whole documentary online
@TomValedro Nice spelling of "prodigies". You clearly aren't in a position to jeer at them.
What can I do to be as good as them?
Do math. These problems are difficult but they arnt impossible. If you were to master the fundamentals, you would see they are using very common tools. They just used the right tools to use at the proper times
Sometimes I wish I devoted my education to math like these people. Without any formal training beyond my high school curriculum, I placed in the top 1% of test takers on the AMC test, and scored a 2 on the AIME. I just wonder where it would have taken me.
@angela1894 Also, you seem to assume that the best student in an American competition is therefore the best in the world, which is obviously nonsense. Math competitions among universities take place in other countries. But the Olympiad is a global contest that pits the best in all countries against each other. Therefore it is far more reasonable to say that the math Olympiad is a greater indication of intellectual prowess than Putnam or any other national competition among universities.
Well it's an 11 years old clip
7089, 103, 1
F... lucky that I was not in the same class with these guy, they made me look stupid.....
No, a more prestigious mathematics university: Harvard. I know for sure Zach and Arnav are at Harvard, idk about Alex and Zeb.
@angela1894 On what do you base this ridiculous assumption? The Putnam contest gives students 3 hours to do 6 questions while the Olympiad is a 4.5 hour contest containing only 3 questions. This clearly means that the Olympiad questions are far more difficult and demanding of deep thinking than the Putnam contest. It may be that your friend Tripathy is more comfortable and adept at easier questions requiring less time than Zhai, who is probably more of a slow-but-deep thinker.
I can math.
Gianni Cedrone I can math more than u bra , burn .
I can meth too. Hold by beer.
It's spelled meth
polygon not polynomial zach abel.
dont want to study math anymore after watching these kids.
Yeah, let's call in the affirmative action activists to get more Black people in lol
No need for affirmative action... just get some HBCUs to step up and coach some black prodigies... just like was done for these guys by grad students at predominantly white schools !!
gang gang
WTF! I am glad that I am thick!
@cloningprocess this is a claim based on observation, if your offended by it i dont care. i have multiple people who can attest to my claim as well. get over it.
gah, what we call a polygon is "act" in English, annoyingly confusing
i wonder if they had always A's in math ^^
They are high school students so they shouldn't have any problems getting full marks in exams for their age group since they can do these imo problems.
@@oneinabillion654 nope you can't say that. I do many hard problems from prmo, and many competitive exams but I don't ever get full marks in school tests. Everyone just mugs up everything and vomits it. And the thing is I'm so adapted to objective type that subjective type is hard 🤣
k
There have been 128,314 views of this video on Saturday 23 January, 2015, at 9:35 am. I worked out in my head that 128,314 divided by 3 = 42,771.333333r.
and the last 3 digits are the first 3 digits of Pi, omg! lol
Omfg!! This cant be real!!!
I used to be great in math...until the alphabet got involved!
This is literally only for people who are interested in math. I was waiting for some good documentary film skills where it would find some common ground with people who don't study math and nope, wasn't there.
Not sure why I was expecting that, but whatever.
Oh wait I know why "Hard Problems is a feature documentary about the extraordinarily gifted students"
Its really about math problems.
preach that my friend, i was math major, i saw pretty much the girls that were in our department, they regurgitate the shit they're taught "memorize", when faced with difficult problem, they start nagging....we the calms dudes in the back, got the solutions got the fuck out
Terence Tao tis he greatest living Mathematician.
@ihateuutube
It's true that Zhai had a good IMO record (arnav only qualified twice), but I still think Arnav is the best because he's become a putnam fellow three times in a row, and he's looking to repeat the feat later this year. This will make him the 8th person to have ever won the Putnam 4 times since the 1930s. Alex Zhai, on the other hand Alex has had two chances to take the putnam (2008 and 2009) and didn't crack top 5. I think putnam is a better indicator of ability than IMO.
i just spent about 25 minutes solving the first problem using rigorus algebraic number theory, i found no need to factor the thing or extract out the common power of two however i did note how u can move the 1 on the lhs to a -1 on the rhs (too simple) in order to determine what quantities are odd or even under certain situations. and knowing your square and power of two sequence helps. y=+/-1 x=infinity, y=+/-2 x=0, so two real solutions and two hyperreal if somehow infinity is integral i guess
ok cool! but why the fuck do they do that
Aww don't cry! I'm sure you won't be cleaning toilets forever... actually I'm not :\
Umm... I hava but a minor complaint to accordingly issue. Question # 6 was way too easy. I didn't even need to write ANYTHING down in order to circumvent the problem correctly. The length of the respective distances btw points are all commensurate and since the subset of polygons included in the problem were all pretty basic, I realized the answer pratically immediately. (Attach one triangle to each side= basically area of p)X2 was what I used to figure out the solution. I'm only in Grade. 8 XD
EpicDuel King Hello there, I didn't understand your marvelous solution. Could you please elaborate a bit? Where does the x2 pop out? Thanks! I assume you are in University now after 5 years. :-)