
U.S. Team Wins First Place at International Math Olympiad - vinchuco
http://wordplay.blogs.nytimes.com/2016/07/18/imo-2016/
======
sctb
Original discussion:
[https://news.ycombinator.com/item?id=12101163](https://news.ycombinator.com/item?id=12101163)

------
nl
The best and most interesting part of this was about how they trained:

"The six student team is then brought together prior to the IMO for a three-
and-one-half-week training program at Carnegie Mellon University, which is
also organized by the MAA.... This year _we also included ten international
students — students on IMO teams from other countries_. We paid for their
airfare, hotel, food and teaching.... _bringing in the international students
gives the top US students peers_. They always tell you — if you’re the
smartest guy in the room, you’re in the wrong room. So we bring in these
peers, who are actually at the same level as these top six. Of course that
increases the level."

~~~
douche
It's like the top women's college basketball teams employing male practice
squads to practice against[1][2][3].

It makes total sense. You have to compete against those that are at least as
good, and ideally, better than you are, to improve.

[1]
[http://www.nhregister.com/article/NH/20110129/NEWS/301299942](http://www.nhregister.com/article/NH/20110129/NEWS/301299942)

[2] [http://www.annarbor.com/sports/um-basketball/male-
practice-p...](http://www.annarbor.com/sports/um-basketball/male-practice-
players-vital-to-the-success-of-the-womens-basketball-team/)

[3] [http://www.knoxnews.com/sports/smithey-men-find-place-
with-l...](http://www.knoxnews.com/sports/smithey-men-find-place-with-lady-
vols-on-practice-court-ep-413355583-360360441.html)

~~~
qq66
Or Netflix sending additional synthetic traffic to their site so that it's
overdesigned by design. (and, when something goes wrong, they can turn off the
synthetic traffic and immediately get a little breathing room).

~~~
parent5446
...I don't think that's a relevant analogy at all.

~~~
allendoerfer
It is almost comically not. It is not about humans, it is not about teams and
it is not about training for a competition. Just about more of something so
you have reserves. He might as well have said: "Leave space in your suitcase,
so you can buy souvenirs."

~~~
thaumasiotes
> Just about more of something so you have reserves. He might as well have
> said: "Leave space in your suitcase, so you can buy souvenirs."

You seem to have missed the point of the practice by a good ways. It's about
making sure your site can handle X amount of load by exposing it to X amount
of load, which you manufacture if necessary. That is the same concept as
exposing your math students to the competition you want them to be trained
against rather than the inadequate competition you happen to have on hand.

~~~
xorcist
> making sure your site can handle X amount of load by exposing it to X amount
> of load

That's called "testing". Most companies have dedicated people who do it every
day. Testing and training is fundamentally different.

~~~
allendoerfer
It's not even testing, because they leave it on in production - at least the
parent said so.

I like this game, so I will play the next round: This would be as if you would
make the contestants wear high-altitude masks and would only allow them to put
them of, when you realize they cannot come up with a solution during the
competition.

~~~
thaumasiotes
Ok, the next round goes: this would be as if you made the contestants train in
high-altitude masks, but they performed without them.

------
lotux
China, 19 times (from the first participation in 1985 until 2014): in every
year from 1989 to 2014 except 1991, 1994, 1996, 1998, 2003, 2007;

Soviet Union, 14 times: in 1963, 1964, 1965, 1966, 1967, 1972, 1973, 1974,
1976, 1979, 1984, 1986, 1988, 1991;

Hungary, 6 times: in 1961, 1962, 1969, 1970, 1971, 1975; United States, 6
times: in 1977, 1981, 1986, 1994, 2015, 2016;

Romania, 5 times: in 1959, 1978, 1985, 1987, 1996;

West Germany, 2 times: in 1982 and 1983;

Russia, 2 times: in 1999 and 2007;

Bulgaria, once: in 2003;[33]

Iran, once: in 1998;

South Korea, once: in 2012.

East Germany, once: in 1968

~~~
dzdt
For whatever reason, the US public education system has not put much effort
into identifying and nurturing gifted and talented students. Probably the
current resurgance of the US in this contest is due to the rise of math
circles, summer camp programs, and the like outside of the school environment.
There was a good article about this last year when the US team won the IMO :
[http://www.theatlantic.com/magazine/archive/2016/03/the-
math...](http://www.theatlantic.com/magazine/archive/2016/03/the-math-
revolution/426855/?single_page=true)

~~~
laxatives
Almost all money flows to support the opposite tail, the lowest performing
students. For example, No Child Left Behind, which every career educator I've
spoken to believes set education in the US back a decade or more.

~~~
jacobolus
Almost all money flows to the worst performers? Not a chance.

About half of public school funding comes from local property taxes, and as a
result schools in rich neighborhoods have dramatically better equipment,
facilities, and staff levels/pay.

There are huge disparities in school funding from one district to another, and
the folks who get screwed are in poor districts, both in remote rural areas
and in predominantly minority neighborhoods in inner cities.

I found this nice map in a google search just now:
[http://www.npr.org/2016/04/18/474256366/why-americas-
schools...](http://www.npr.org/2016/04/18/474256366/why-americas-schools-have-
a-money-problem)

* * *

The No Child Left Behind law was emphatically _not_ about diverting extra
money to poor performing students, I don‘t know where you got that idea.

~~~
freyir
He's saying resources are spent on the worst performing _students_. For
example, classroom time spent getting the lowest performing students to pass
the (relatively low) bar set by statewide exams.

~~~
jacobolus
That’s also nonsense, unless you’re talking about extra staff time spent on
imposing power/discipline on people who don’t want to be there. In which case,
sure... but what else would you propose the schools do? (Also, this doesn’t
tend to help the students being disciplined all that much, in my limited
anecdotal experience as an outside observer.)

Some students get extra support because they have disabilities or need extra
language instruction. This is not about poor performance, per se, but rather
about giving extra support to specific groups of students who obviously need
it. This usually relates to state/federal law.

But your run-of-the-mill poorly performing student is given woefully
inadequate support by understaffed and underfunded schools, just like everyone
else. The way to fix this problem is by improving teacher pay, giving teachers
more time during the schoolday but outside the classroom for self improvement
and collaboration, properly supplying schools and fixing their facilities, and
giving teachers more local autonomy and less bullshit standardized tests.

The best performing students tend to get tracked into special classes
(“honors”, “AP”, etc.), have more direct relationships with teachers, are
members of school-organized extracurricular activities, and so on. They speak
up more often in class, interact with other academically motivated students.
Perhaps most importantly, they generally have more considerably more external
support (family help from better educated parents with more free time, private
tutoring, out-of-school music/art/sport/etc. training, and so on).

~~~
freyir
NCLB set minimum performance requirements for basic skills. It tied school's
funding directly to the performance of its lowest achieving students. In my
personal experience, teachers regularly stopped their regular curriculum and
focused exclusively on test prep in the weeks leading up to the statewide
exams. Even in honors classes, where you'd expect every student to demonstrate
basic reading and math proficiency, we stopped our normal studies and did test
prep.

Did this have an negative impact on gifted program funding? Some educators
definitely believe it did.

"In particular, NCLB does not require any programs for gifted, talented, and
other high-performing students. Federal funding of gifted education decreased
by a third over the law's first five years ... In other states, such as
Michigan, state funding for gifted and talented programs was cut by up to 90%
in the year after the Act became law."

~~~
soundwave106
I'd be surprised that teachers in advanced programs would actually stop to
focus on state exams or NCLB type tests? Back when I went through IB (over 20
years ago, granted), the state test was almost an afterthought. Most of the
people in those programs if I recall breezed through those tests in no time,
and had the remainder half a day or so to leisurely do what they want.
(Obviously instead a lot more time was spent preparing for the IB and AP
exams).

Half-baked measures like NCLB (eg, make schools "accountable" and they will
somehow improve magically) does nothing to resolve the "environment gap",
which in my opinion is probably one of the most critical factors in academic
performance these days.

------
allendoerfer
All perfect scores from people of Asian descent. 1 person not of Asian descent
in top 20. First girl is 63rd.

~~~
methehack
If you haven't read Malcolm Gladwell on Rice Farming and math you really
should give it a look: [http://gladwell.com/outliers/rice-paddies-and-math-
tests/](http://gladwell.com/outliers/rice-paddies-and-math-tests/)

~~~
darawk
You could just as easily turn that around, though and say that Asians have
better systems for numbers because they are _inherently_ more gifted at
numerical manipulation. But either way, winning the IMO has very little to do
with calculation ability anyway.

~~~
methehack
Seems like I should clarify... It may be that Asians are just better at math —
“inherently” as you say. Ok, maybe.

It also seems possible that there are certain aspects of language and culture
that support math achievement. Gladwell, in _Outliers_ is after this category
of explanation.

Personally, I tend to like cultural explanations more than raw talent
explanations because I like to think that everyone is capable of everything
(eventually, if they work hard enough). I certainly like to act like everyone
is capable of everything and it helps to have supporting theories.

Gladwell’s theory goes something like this: First, the counting systems tend
to be more consistent, less idiosyncratic. This means kids learn them better
earlier and build confidence early. This early start builds on itself — a
point he comes back to over and over in his book. Second, the numbers tend to
be faster to say. This means you can remember more digits — quite a few more.
This has the same impact on confidence. Third — and this is his main deal —
rice farming yields to careful, persistent effort much like a math problem.
This is less true of western farming. All the western farming sayings go
something like “there’s no accounting for the weather. sometimes your just
eff’d!”. All the Asian sayings go something like “work hard and your family
will prosper for generations.” He says this gives Asians a leg up in math
because math yields to the same kind of persistent effort.

Also — someone below diss’d on Gladwell calling him a “pop” psychologist. I
don't think he is not a psychologist, though I guess he is pretty pop. Still,
what he does, while researched, is not science, that’s for sure.

I think explanations like Gladwell's are valuable even if they are not true
because they at least show us how nuanced and twisty the truth might be. That
keeps us looking for explanations that are maybe not so simple. That's good
because as a species we're stupid enough without the crippling detriment of
thinking we already understand what we do not.

EDIT: very minor for clarity.

~~~
umanwizard
What you "like to think" is irrelevant because reality isn't here for our
benefit.

~~~
algorias
This is not a very nice way to formulate your objection, but I have to agree.
Believing things because you'd like them to be true is a terrible way of
trying to get at the truth, and the arguments for that position are the most
contorted I've seen in a while.

------
tuna-piano
How much of mathematical intelligence genetic or environmental? It seems to be
at least a fair amount genetic. After all, the brain is a body part like any
other. Height is genetic, so why wouldn't physical brain characteristics also
be?

It is remarkable the amount of asian and male students in this top echelon. It
could be because of societal influence - but that really seems unlikely to me
to cover this huge gap.

It may be unsavory, politically taboo, and not the way we want the world to be
- but are males and people of asian-ancestry just better at math? And would
knowing if that is the case help anything in any way?

~~~
dannylandau
I'll take a shot at this (your bait). For context have an undergrad in Math,
my parents are mathematicians and theoretical computer scientist. Read quite a
few biographies on famous mathematicians, and one salient inescapable
conclusion is that the most prominent mathematicians tend to be European or
American, and very rarely Asian (chinese, Korea or Japan). There are of course
exceptions, but few. The top mathematicians are not Asian, just a fact. And
yet, the majority of IMO gold winners are, not sure how to explain the
discrepancy, but the most likely conclusion is that solving Olympiad math
questions has very little correlation with with doing creative mathematics.

~~~
chillacy
> The top mathematicians are not Asian, just a fact

Alright I'll bite as well. Though I don't think the OP's conclusion is
correct, I also don't think the lack of prominent asian mathematicians is
entirely indicative of ability or creativity, but rather largely caused by the
availability bias of English speakers and our current vantage point in
history.

First: availability bias. We're reading English books and working within an
education system born out of Europe. Asian history has been full of
interesting wars, rulers, artists, politics, etc for thousands of years, but
few in America will ever learn anything except for where it relates to America
/ Europe. Much of the information about Asian history will be in another
language as well.

Second: Recent history. Knowledge-creators in other countries are playing a
game they are disadvantaged in, having to first learn English, then travel
abroad for the best universities, etc. (Imagine if you had to learn Japanese
and travel to Japan to go to get a decent higher education!)

The reason of course is that 1500s and onwards (post-renaissance), most of the
knowledge generation was happening in Europe. But that wasn't always the case:
if we look a thousand years prior, or 2 thousand years prior, knowledge was
being generated by Greek, Arab, or Chinese mathematicians. For instance, the
concept of 0 arrived to Europe pretty late:
[http://www.livescience.com/27853-who-invented-
zero.html](http://www.livescience.com/27853-who-invented-zero.html)

So circling back to the original question of the importance of genetics vs
environment:

That the world's patches of knowledge has shifted across different cultures,
peoples, and places over the last maybe 8 thousand years to me doesn't imply
such a large importance on inherent genetic ability, and that time frame is
too short for any evolutionary changes.

Culture seems to be a much larger factor (and this is where I will concede
that asian culture can stifle creativity). Culture is the main difference
between the heads down religious conviction of the 9th century in Europe and
the renaissance, not genetics.

~~~
jernfrost
I also don't believe there is a genetic difference, however I think there is a
clear cultural difference which favors westerners. Asian culture with its
emphasis on harmony and respect for the elders does not IMHO foster radical
innovation. A key problem for China is that it is united. This stifles
competition in ideas of how to organize society. Europe has benefited
tremendously from being divided. That has prevented Europe from stagnating the
way China did for hundreds of years. One stupid ruler can bring down all of
China. One stupid European leader can't bring down the whole of Europe.

It is also false to consider Europe being a laggard in earlier times just
because it was behind in maths and higher learning. One tends to think the
Roman empire was so superior due to its progress in the arts and sciences.
However medieval Europe saw far more progress in e.g. machinery and labour
saving devices. Windmills, waterwheels, better plows etc was developed in this
period.

In the short term the unit of China reaped a lot of benefits in the form of
having much more peace. Europe suffered many setbacks due to the frequency of
wars. But in the long run this proved a benefit. The fierce competitive nature
of westerners could not be countered by harmony focused asian cultures.

~~~
chillacy
Yes, competition tends to be bad for most individuals (who lose) but good for
society.

China of course started taking off recently too after capitalist reforms in
the 80s. The US, arguably one of the most "pull-yourself-up-from-your-
bootstraps" of nations has done pretty well, despite lack of social programs.
And back to Europe, I do think it was held back due to the forced conformity
to the Church (IMO Christianity held back European science for hundreds of
years).

So yes, culture is a very big current as far as steering people!

------
liamuk
Interesting thing I heard from Po once:

The key to the American team's recent success is forgetting about the IMO and
just learning math. Instead of teaching mechanics-- techniques specifically
for solving olympiad problems (as they had done a lot of before, and as many
countries do), the idea was to just show interesting and fun things from real
math and build strong intuition for mathematical problem solving through that.
If you look at lecture's he's given in the past at MOP:
[http://www.math.cmu.edu/~ploh/olympiad.shtml](http://www.math.cmu.edu/~ploh/olympiad.shtml),
you can see they're mostly just highlights from his area of research.

When he was being considered for coaching he told the MAA he would run
training for the IMO team in a very different way from how it was done and how
and that choosing him would be a gamble: there was a chance that it would go
spectacularly wrong. The gamble has seemingly paid off.

It's also nice that this is a quintessentially American way of doing things :)
Just pursue what you find fun and it'll pay off. Don't over-optimize for the
accolades.

~~~
fspeech
While Loh's approach is commendable that is not necessarily the approach the
kids follow to be selected. IMO is kind of artificial in its subject matter so
it is not true that the more math you know the higher your odds. These kids
have trained very hard on their own (you have to be obsessive to get to the
competitive level), just to be selected. My guess is that Loh's approach kind
of loosen them up instead to giving them more of the same of what they already
did on their own and this seems to have worked wonders for the highest
performing kids.

~~~
liamuk
This is probably true. Still, a nice idea.

------
curiousDog
Reiterates the fact that the strength of America is its diversity and openness
to attract and retain the brightest from around the world.

~~~
United857
Judging from their names, most of the US team members are of Chinese or Indian
descent.

Would be interesting to note if they were US born/raised (i.e. educated under
the US educational system), or recent immigrants (i.e. primarily educated in
those countries).

~~~
pcurve
I would guess that they were born here, or came here as a very young child.
You'd need to have fairly good mastery of English to correctly interpret those
questions.

~~~
Swizec
I came here at 26. My English tests at native levels or above (it's been ~10
years since I took the test). Most people assume I'm a native speaker until
they hear my accent and even that is going away.

English really isn't that hard to learn.

~~~
gone35
Idiomatic English _is_ hard. From your HN profile[0]:

"At least 5000 people bought my books..."

Don't ask me why, but to me it should read instead:

"at least 5000 people _have bought_ my books,"

or even:

" _over_ 5000 people _have bought_ my books."

[0]
[https://news.ycombinator.com/user?id=Swizec](https://news.ycombinator.com/user?id=Swizec)

~~~
dasfasf
Just "bought" implies that the sale of the books is compassed in the past. It
sounds strange because no explicit compass is mentioned and the reader
suspects they are still for sale. I don't see anything wrong with "at least"
though. Note that "over" changes the meaning (>= vs. >) and at least some
prescriptivists obelize using "over" like that (I believe the AP Stylebook
used to).

~~~
gone35
_[...]and at least some prescriptivists obelize using "over" like that (I
believe the AP Stylebook used to)._

Indeed they did, until very recently[0]. I had no idea.

[0] [http://www.quickanddirtytips.com/education/grammar/more-
than...](http://www.quickanddirtytips.com/education/grammar/more-than-vs-over-
a-big-change-at-the-associated-press)

------
jtchang
Po-Shen Loh is a complete badass. You're the best in the room until Mr. Loh
goes and finds a tiger for you to wrestle with.

------
dannylandau
This question has come up before, but never found a suitable answer -- anyone
has a list of notable alumni that have participated in IMO that have gone on
to do great things in life?

~~~
stedalus
[https://en.wikipedia.org/wiki/List_of_International_Mathemat...](https://en.wikipedia.org/wiki/List_of_International_Mathematical_Olympiad_participants#Notable_participants)

------
adventured
I'm always fascinated at how common it is for people (almost universally
cynics from outside the US) to try to discredit the US winning this
competition by proclaiming that the participants aren't really Americans,
because they're of some other ethnicity than white. It usually goes like this:
'well, they're mostly Asians, so it doesn't count.' I saw it constantly with
the US winning last year's International Math Olympiad, and I'm seeing it
again on various forums this year. Often it comes in stealth form, they'll ask
intentionally leading questions about where the competitors were educated, or
where they were born, trying to avoid being too blatant about their racism and
or anti-US cynicism. Some people just can't stand for the US to do well in
anything.

~~~
allendoerfer
I think they are Americans. It is not like countries are buying children to
win at maths competitions as some do with athletes for the Olympics [0]. It is
just notable that they are all of Asian descent. It is also notable that they
are all male. You are not instantly racist when you realize that a group that
represents a country at a competition or the overall starting field of a
competition has different characteristics than the general population.

[0]: [http://www.telegraph.co.uk/athletics/2016/07/07/seven-
kenyan...](http://www.telegraph.co.uk/athletics/2016/07/07/seven-kenyans-two-
jamaicans-and-a-cuban-competing-for-turkey---t/)

~~~
adventured
The racism isn't from noting the race, it's from attempting to proclaim that
the competitors are not Americans due to their race eg being Asian. As an
example, that claim was made up and down the threads on Reddit about last
year's US Olympiad win.

~~~
Alex3917
The U.S. does have a long history of importing foreigners to win competitions,
so it's not really an unreasonable suspicion. E.g. a large percentage of
athletes at Harvard are from Canada or eastern Europe, since their grades and
SATs don't get included in the U.S. News & World Report rankings.

~~~
douche
Harvard does have good hockey teams

~~~
yompers888
Rowing, too. It's substantially harder to win races when your school isn't
allowed to import eastern Europeans for that purpose.

------
rawnlq
I found his claim that "people are basically the same" pretty interesting. He
came from a family of IMO medalists (himself, his brother Po-Ru Loh, and his
sister Po-Ling Loh). So it's surprising that he believes in nurture over
nature.

Maybe there was really some secret sauce in his upbringing that he is now
passing on via coaching?

~~~
cjbprime
Is it surprising? Intelligence isn't 100% hereditary; maybe 50% can be
attributed to genetic factors? So if you see three family members performing
at world-class intelligence levels, you might actually be experiencing a
nurture argument, not a nature argument. The heritability of intelligence
isn't strong enough to explain that outcome through nature.

~~~
yompers888
Another front page thread tonight has multiple people saying it's 0.4
hereditary at childhood, rising to 0.75 by adulthood. Height is 0.8. I take
those numbers with healthy skepticism, having not read the source material,
but they aren't out of thin air.

~~~
splouk
Could you link me that thread?

------
shriphani
Po Shen Loh is one of the most inspiring math professors in the world. Pure
passion for math instruction and high quality math research.

While he's in charge, expect the US to produce several medals at the IMO.

~~~
ausjke
One key action he initiated is to put F-1 visa high school students to the IMO
team, basically he is using top students from China to compete, a practice
that the physics and chemistry Olympiad do not take.

And guess what, that's the key to win.

------
netheril96
That many of them is of Asian descent has been mentioned a lot. Perhaps the
top US universities should reconsider their soft cap of amount of Asian
students admitted every year.

~~~
chipperyman573
While I agree with the argument you're making, you can't exclusively use this
as your evidence.

~~~
tluyben2
There must be research into this? I am from west EU and east EU always did
much better in math. I had a few companies over there and my colleagues there
told me that you study to make money which means you won't study music,
languages, history etc. In NL where I grew up, people basically studied for
fun and 'the job' comes automatically; I guess (!) Asia would be the same
mostly?

------
socrates1998
The US director inviting the other people from around the world is brilliant.
A great way to train your team by helping others.

And the dominance of Asians is interesting. It's a very cultural thing.

I can't remember who proposed it, but the idea that East Asian languages are
much easier to learn basic counting is interesting.

The idea is that Chinese, Korean and Japanese all have easier languages for
counting. This gives young Asian students a small, but real advantage when
first learning math that accelerates as time goes on.

I would be interested to see how many of the top math Asian-American or Asian-
Anglo students know one of those three languages or not.

If a lot of them have zero knowledge of Chinese, Japanese or Korean, then
clearly this idea is dead.

~~~
_nothing
I first saw it discussed in either Malcolm Gladwell's "Outliers" or Dubner and
Levitt's "Freakonomics". They sort of blend together in my head because I read
them both over the span of a couple days and they touched on really similar
themes (which I hadn't expected), but I suspect it was the former.

Wherever I read it, they listed it as just one of several reasons Asians tend
to be good at math, with cultural factors being another important factor.
Something about how, while Westerners generally had to just plant wheat and
similar crops at a specific times and they would grow fine with a base amount
of effort, the yield of a rice paddy was directly related to the effort put
into maintaining it. According to them, this ingrained (hah, grain) into Asian
societies the idea that your success is directly proportional to the effort
you put into something.

I haven't studied it myself, but I thought that theory was interesting.

~~~
socrates1998
Yeah, I don't really by the "they planted rice and it was tedious, therefore
they are good at math."

For a long time, Westerners were dominant in math.

It's only very recently that we have seen East Asians doing well. And, I don't
know that it persists at the graduate/top level, it may only be at the high
school and undergrad level.

I mean, East Asians have been growing rice for a really long time, so why does
it mean now they are good at math.

Who knows, it's an interesting phenomena.

------
flashman
Since nobody has tackled this so far: what are the answers? And more
interestingly, how do you get them?

~~~
Cogito
For problem 3, you can start as follows:

(1) The points of the polygon are inscribed on a circle. [given]

(2) Construct a triangle on each side of the polygon with the centre of the
circle from (1) as the third point.

(3) Each triangle from (2) is isosceles. [2 of the sides are radii of the
circle from (1)]

(4) The area of an isosceles triangle can be given as _1
/2a^2sqrt((b^2)/(a^2)-1/4)_ where _a_ is the length base of the triangle and
_b_ is the length of each of the other two sides. [proof left to the reader!]

(5) The square of each side of the polygon is divisible by _n_. [given]

(6) For each triangle from (2), double its area is divisible by the square of
the side it is built on. [from (4), (6.1)]

(6.1) _sqrt((b^2) /(a^2)-1/4)_ is an integer. [proof missing]

(7) For each triangle from (2), double its area is divisible by _n_. [from (5)
and (6)]

(8) The area _S_ of the polygon is equal to the sum of the triangles from (2).
[by construction]

(9) If _n_ divides _a_ and _b_ then it divides _a+b_

(10) _2S_ is divisible by _n_ , QED. [from (7), (8), and (9)]

Of course, this is not complete.

For example, we also have to show that _2S_ is an integer, which really comes
down to showing that _sqrt((b^2) /(a^2)-1/4)_ is an integer. I should add,
this is also needed for (6) as if that statement is not an integer than (6) is
false.

[edit] I've added the missing step (6.1) though it is incomplete for now.

[edit 2] Actually, the missing step is different! The sum of the (6.1) pieces
from each triangle needs to be an integer, not each individually (though if
you could prove individually than you would get together, obviously).

[edit 3] I'm silly! We know that _2S_ is an integer because of the general
form of the area of a polygon, given vertices (x_1, y_1), (x_2, y_2) etc. That
is:

 _S=1 /2(x_1y_2-x_2y_1+x_2y_3-x_3y_2+...+x_(n-1)y_n-x_ny_(n-1)+x_ny_1-x_1y_n)_

As each _x_ and _y_ are integers, then _2S_ is an integer.

There are still issues, because (6) is still not known to be true (and in fact
may not be true at all)

------
ak39
I opened the link to the full question paper. I'm amazed at the level of
complexity in the wording of the questions themselves. It looks like the real
challenge is understanding the questions first. What are they asking? Applying
math and logic is probably just as important but I feel that can only follow
if you grok the crushing English/language.

Which begs the question: do translations into other languages confer any
advantages?

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signa11
honestly, NK scoring 168 is very impressive, imho.

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euske
So this clearly shows that boys are much better at math than girls. Period.

Or not.

Sometimes I wonder if these competitions (or the real Olympics games for that
matter) lead to a more racial/social prejudice, rather than diminishing them.

~~~
az0xff
Competing at the top level of any sport (athletic, mental, or otherwise)
requires the right training and support almost as much as the right mindset,
work ethic, and talent. The training and support requires time and money.

At present, people of different ethnicities have a disproportionate share of
wealth, and thus fewer resources that they can spend on training and support.
Support begins early: parents help their children find the right activity to
undertake and also teach them the mentality to work hard at it in order to
compete -- this is almost impossible to accomplish if those parents have to be
away most of the time because of financial constraints.

As for gender, we have only recently entered an era where we recognize that
girls are equally capable of doing things like math at a top level (the first
Fields Medal given to a woman was given to them quite recently). In girls'
formative years, parents still have some subconscious expectations of what
their children are capable of -- perhaps being reluctant to expose girls to
the sciences or other serious undertakings. There are some recent efforts to
get girls into these things, but the fact that they are newsworthy proves that
it's not the norm yet. The time that there will be equal female representation
in these areas will be when an entire generation understands that women and
girls are equally capable of getting into them. This will be after everyone
who comes from the previous era of society have died.

~~~
SamReidHughes
Your theories would be plausible if the number of girls competing at a close-
to-top level wasn't outnumbered by the number of boys who by any life-
background metric would have no business being there. I'm talking about
trailer park kids, poor immigrants, schizophrenics, and absolute slackers
here. It will take some training and practice to get on an IMO team -- because
your competition is doing so -- but at levels below that, girls are
outnumbered by boys making no special effort in math that just show up and get
high scores on contests.

Realize that anybody that would be at, say, top-500-high-school-students-in-
USA math level will be the sort of student that coasts through all their math
classes from K-12, with the typical schedule taking pre-calc in 10th grade,
with no studying and no stress at all, easily the best in their class,
assuming the school system just ignores their talents. There would have to be
250 girls in this situation, of which those that finish over the top 500
threshold on things like the AMC or AIME or earlier contests are outnumbered
by boys with less "support" that just show up and get high scores on math
contests.

Also, in my experience in middle school there were many girls that were quite
competitive in 24 game, that just disappeared in more mathy contests like
MathCOUNTS.

------
known
Due to
[https://en.wikipedia.org/wiki/Peer_pressure#As_a_leadership_...](https://en.wikipedia.org/wiki/Peer_pressure#As_a_leadership_tool)

------
sergers
[https://twitter.com/urbanstrata/status/753932591514787841](https://twitter.com/urbanstrata/status/753932591514787841)

~~~
dudul
I don't have a problem with the team, but how does this tweet make sense? They
are all (except one apparently) Asians, in what dystopian universe is this
"diversity"?

Sometimes I feel sad that we took a nice word "diversity", and perverted it to
mean basically "anybody except white males".

And just to be clear, if these guys are on the team it's probably cause they
are the best, so they all deserve to be there, and I wouldn't want to kick 2
of them out just to add a girl and a white guy.

------
philip1209
That's great, but we shouldn't judge the state of education in our country
based on outliers.

~~~
jkw
No one was suggesting that?

