I hope not. Because I have definitely gotten some math problems from my daughter’s 6th grade class “wrong.”

Ok, ok, I put “wrong” in quotes. See? I did it again. Why?

Because the problems I get wrong are the ones that either rely on definitions that no one uses in real life, are based on definitions that are vague, or are ill-posed questions.

Let me give you an example from way back in 2nd grade of what I mean by a bad definition. One day my daughter was asked to identify the “lines of symmetry” of a set of shapes, where “lines of symmetry divide the shape into two parts that are the same.” (Edit: expanded the range of the quotation marks for clarity) So, for example, the dotted lines below are each lines of symmetry of the square:

Meanwhile, here are the lines of symmetry of a rectangle according to the 2nd grade class:

Can you spot the problem?

The diagonals of a rectangle also divide a rectangle into two parts “that are the same” — specifically they are congruent. So the diagonals should also be lines of symmetry, according to the definition used.

It turns out, the whole time the school meant “lines of mirror symmetry.”

So it is, in fact, quite easy for a mathematician (or in my case, a theoretical physicist) to get the wrong answer on even a 2nd grade math problem. I feel no shame about this at all. This actually happens fairly often - often enough that her 6th grade teacher has asked me, essentially, to stop looking at her homework. I haven’t yet decided if I will.

EDIT: P.S. As pointed out in the comments, all lines through the center of rectangle divide it into two congruent parts. I am aware of this but didn’t want to overcomplicate the answer.

Well, try your hands on *this* one.

[Translation: Five-star difficulty; Find the area of the shaded region (units are given in cm); 6th graders, five star difficulty]

This is one of the problems that once got famous in China as ‘elementary school problems’. Another one, e.g. is a Diophantine equation involving cubic curves which ‎Alon Amit (אלון עמית)‎ once analyzed.

(It is suspected that the downleft corner has an area unshaded by mistake.)

Of course. That’s the point of them being math Olympiad problems: they are very challenging.

Perhaps the assumption is that a challenging problem for a high school student must be a walk in the park for a graduate student, or a Ph.D. holder, or a mathematician in an academic position. This isn’t so. Problem solving is an important part of math research, but it’s not quite the same kind as Olympiad problem solving, and earning a Ph.D. in math takes skills and dedication of a different character.

Some mathematicians enjoy Olympiad-style problem solving and can handle many Olympiad problems faster than you or me, but many don’t, and even the best of them may not be able to earn top scores at a recent IMO. The kids who participate at the IMO are deeply immersed in this style of problems, they are well trained, and they have just the right type of smarts for this challenge: creative structuring of strategies, blazing fast assessment of different ideas and directions to pursue, tenacity, imagination and a keen sense of abstract analogies.

All of these things are useful for math research in general, but Ph.D. students don’t have to be as crazy athletic at them as the Olympiad kids are. By way of analogy, think how well most professional sportspeople – say, NBA players – would do at the majority of summer Olympics events – say, artistic gymnastics.

(…)

Yes, of course it does.

If you’ve reached the point where you can routinely solve a good portion of the problems on the International Math Olympiad, then you’ve mastered a pretty deep creative skill. When you look at an IMO problem, you don’t feel as mystified or mortified as you once were. You’re not confused. You have ideas, you have approaches, you’re comfortable, even excited.

You now know what problem solving is like. You know the common initial feeling of “ok I have no idea where to even start”, and you’re not afraid of it. You know the common feeling of “wait, this can’t be true…”, and you know how it breeds understanding when you think about it more. You know you may need to try sixteen different approaches before you hit the right path, and you’re not afraid of that either. You have a reflex to pursue analogies, however vague. You instinctively look for small, simpler steps to start with, or for ways to break the problem into more manageable chunks. You know how to backtrack when you hit a wall, and try a different way. You do these things easily, almost unconsciously. You’re a confident problem-solver.

You’ll do the same things when confronted with a challenge outside of math, even very far from math. You may be writing a poem and hitting a dead end with the rhyming structure. You may need to deliver a presentation in 24 hours and don’t even have a draft. You may have forgotten to call your mom on her birthday. You may be unsure which job offer to pick. You may have lost your car keys. You may have lost your love.

The confidence you’ve built in knowing that you can solve seemingly unsolvable problems will serve you well in those cases. Specific strategies will often be surprisingly applicable. Your skills of abstraction will delight even you. Your ability to frame a coherent argument will be an asset. You may find yourselves solving real-life problems that seem insurmountable.

And, of course, your IMO solving prowess will thoroughly impress your love interest.

At the risk of stating the obvious: Learning to solve IMO-level problems is far from the only way to acquire those skills, and not necessarily the best way for you or anyone you know. Do it if you’re attracted by it, but don’t force yourself to learn math just because someone on the internet said it will help you in life.

The way they teach math today is completely confusing and unintuitive. When I was in my MD/PhD program, a friend from graduate school showed us her daughter's homework. Two MD/PhD students and a PhD student couldn't figure out any of the problems, and all of us were doing quantitative research at the time. The definitions they use these days don't match the mathematical definitions you use in mathematics, and I can't imagine these children learning the real definition of the words in later mathematics courses without a lot of difficulty changing their way of thinking about a word that was drilled into them as a child. This is probably why we have a shortage of mathematicians. If something is taught in a way that is confusing and unintuitive to children with mathematical talent and reasoning skills, they'll learn that they hate math and aren't good at it.

Yes, I could solve probably any of the problems on the homework. But I would get a 0 for not solving them the way the books says a student should solve them. And I have seen children of math folks getting 0's for solving it the way their parents' suggest it should be solved because it does not match the current math teaching philosophy and the steps the books says one should use. I have gotten 0's on homework for this, as well, when I was growing up. Linear algebra makes a lot more sense for solving systems of equations than the weird pseudo-math taught in pre-algebra.

In mathematics as field, someone who comes up with a new way to solve an old problem that cuts out unnecessary steps is given awards for achievement. A student who does this in middle school is given a bad grade and told they are bad at math...

Greetings

The answer to the question has been provided in quite a different method, just as humor as is purely hypothetical.

Let us assume that there are N mathematics students who are to appear for the IMO. For each question to be answered by a candidate, there are five possibilities:-

i)He can completely solve the problem to get the answer

ii)He can partly solve the question, but can guess the right answer

iii)He can partly solve the question, but cannot guess the right answer

iv)He cannot solve the problem, but can get the answer through rational judgment of the options

v)He can neither solve the problem nor guess the right answer

In the question it has been said that the student can't solve the problem, which means he cannot get the answer at all. Keeping this point of view, condition (iii) and (v) could probably be taken for the failure of the random experiment of solving an IMO problem.

Let each of the above conditions be assigned equal probability, ie, 1/5. Then, success the experiment includes conditions (i),(ii) and (iv).

Hence P(success) = 3/5

Subsequently, P(failure) = 2/5

Let us first calculate the probability for N successes(as there are N students).

By Bernoulli trials, we have, P(N successes) = (3/5)^N*(2/5)^0

So, probability of N successes is (3/5)^N

Then, P(N failures) = 1-(3/5)^N

Hence, in an IMO exam with N mathematics candidates, the probability that a student cannot solve an IMO problem is 1-(3/5)^N.

Congratulations for your mathematical abilities :)

The answer here is interesting.

First let me tell you that I didn’t make it into math olympiads in highschool (mandatory participation) simply because I wasn’t doing a thing. Yet I finished first at my university for five years, and went on to Cambridge. So everything is a question of work.

I doubt that you spend 6–10 hours in front of your sheet. You probably take breaks, do something in between.

Have you noticed how the answer often comes when you least expect it, that is, when you are not thinking actively about the problem ?

What you need is to let your brain do ‘subconscious’ (for lack of a better word) work in the background.

If you have four problems to do in 8 hours, spend one hour on each problem (or more if you see the solution). Then go back to the first problem, and so on. This way, you leave your brain three hours to think of alternatives while you are busy doing something else.

I can’t tell you exactly why, but we tend to stay stuck by our own, unconscious, implicit hypotheses.

You probably know all too well this problem :

The answer is not that hard, when you go out of the implicit frame of staying inside the square. Most people don’t realize those assumptions (staying inside the square) they do all the time.

When you actively don’t think about the problem, somehow, those assumptions can be removed.

The other important element would be to train yourself as much as possible, and to try to abstract the thought processes that lead to the answer. There are, in general, families of problems that will be solved in similar fashions. If you encounter many original solutions, and really think hard about how you could have thought about it (ex. which questions you should ask yourself to think of the next step), then you can start to make links when encountering new problems, with your previous knowledge.

I highly recommend russian textbooks (olympiads, arnold,…).

PS : you might be interested in my book ;)

Yes, of course.

When my son took Differential Equations, I had to look back at how to create an integrating factor, but otherwise could do any undergraduate math problem. I even helped a college student riding along with us with her Calc II homework while I was driving.

The biggest issue is making sure that you show methods that their HS teacher is familiar with. Not all HS math teachers even have a Bachelor’s degree in math, some just have a minor. I had teachers in Elem and HS who did not like it when I knew things that they had not taught me, either in math or in science. I did not have that problem with college instructors, as they encouraged independent learning.

My kids had good math teachers, but I would make sure that they understood the techniques that they were studying. I would also show them an alternate method if that other method was more broadly applicable.

For example, the FOIL method is an acronym for how to multiply two first degree polynomials together, in HS typically for two polynomials in a single variable. I would show them an easy and faster way to handle multiplying two polynomials in single variable together of any degree. This also was a way to show them how to handle multiplication in any base.

No, absolutely not.

IBO and IChO materials are covered in undergraduate Biology/Chemistry courses, but their problems are significantly harder than the homework/exam problems in the corresponding college courses. If an undergraduate student can solve these problems, he/she should be considered excellent, rather than average.

IMO and IOI materials may not be covered in university-level Math/CS courses. You can get a degree in these disciplines without touching anything involved in the corresponding Olympiads. Hence, being an undergraduate student would give one little or no advantage over a high school student at all.

IPhO is kind of in between. Still an average undergraduate would have no chance.

Go for it! This absolutely would not be waste of time. You never lose when you learn.

Most IMO problems does not require much background. The problems are usually easy to understand and start thinking of possible solutions. IMO problems are divided into 4 major fields: Algebra, Combinatorics, Geometry and Number Theory.

As a student you probably found the area you’re passionate about. If this is your case then take a look at the IMO Shortlist problems of your chosen subject. If you are still undecided and want to explore the beauty of all 4 fields, then start with problems 1 and 4 of IMO contests. First problems of each day are not too complicated but it still might take a while to see the idea of the solution.

My main suggest would be not to give up (and look at the solution), if you could not solve a problem in 15 minutes. Try to do your best; come back after a while, if not succeeded. Solutions are available, but use them wisely. Look at solutions only if you feel that you are really done, then it should be really easy to understand the solution.

P.S. Some people solve these problems within 30 minutes, others need to spend many joyful hours for each problem. This is a measure of speed, not measure of problem solving ability.

I have a controversial answer to this:

It is because humans are only barely smarter than other apes.

"What?!" you say. "We went to the moon! We invented epistemic logic! We are unraveling the very laws of the universe!"

True, but you don't need to be particularly smart for that. I believe we achieve all these things mainly by our other qualities:

• Excellent communication skills. We have evolved to talk. Humans learned to read and write (which took us long enough by the way). Once someone comes up with an idea and writes it down, we can put it in a book and start teaching it in schools. We memorize the good ideas of the past. Experts at any topic can tell us how to think and what to practice; we practice it for a while and we start to understand the things they learned to understand. No (or not much) creative thought is required anymore, and the leaps of insight we do have occur slowly.
• Excellent memory. We remember an incredible amount of information, and we slowly but surely process that information, and every now and then we make one or two new connections. We are not good at seeing through something complicated, but after working on a topic for a while we build up a network of connected ideas that lays the foundation for finally understanding the problem.

So in my view, humanity's achievements are fundamentally the product of a very very slow, but very long-running, accumulation of cultural accomplishment.

Of course, some humans are smart relative to other humans. Most humans are smart relative to apes. But from a distance, I think we probably look like a cat that thinks it's big because it has never seen a tiger.

You may not agree with me now. But watch for it. The signs of human stupidity are everywhere. The next time you fail to see a completely obvious connection, don't see the solution to a puzzle that is, in hindsight, embarrassingly simple, then think: what do you really expect of a species of arrogant apes?

In my day and school, we didn’t have the Math Olympiad per se, but Canadian schools had the Junior and Senior Math Contests, the Junior one being produced by the Faculty of Mathematics of the University of Waterloo, while my memory fails me for the Senior one, other than it had to be marked by hand while Waterloo’s was marked by a computer. I was invited to take part in the Junior one in my first year of high school by the teacher who managed it locally - he specifically called me out of class to tell me about it.

In those days, the Junior one was for students in Grades 9 through 11, but nearly all that wrote it were Grade 11. The Senior one was actually open to anyone, but they generally had students in Grades 12 and 13 (we still had that in those days) trying it. The questions were never just math from the comparable classroom, but problems needing the student to figure out the mathematical considerations needed to get an answer. Some were more challenging than others, but rarely did they dive into anything needing esoteric theoretical mathematics. If anything, they often ended up being solved with math that should have been mastered by Grade 7, once you understood what the problem represented mathematically.

Some people live with working out complex multi variable equations on a chalkboard or wipe board representing matrices and eigen vectors with nearly no standalone defined values as part of Ph.D. or D.Math theses. Some develop mathematical models of theories or propositions coming from other disciplines, such as physics or economics, or extrapolate on existing ones to find theoretical real world impacts (or divergences). These are single questions where the properties and mathematical principles are worked with at length. Math Olympiads are being able to craft mathematical models on the fly, and understanding the applicable properties of the numbers involved, in a short amount of time. These are not going to be complex models necessarily, but they are drawing on enough knowledge to perceive possible values that find a solution, and possible pratfalls that can result in wrong answers.

The Junior Math Contest, I remember the first year there being people close to tears not knowing the answers, and it was multiple choice. Me, I have always had a knack for multiple choice tests as the answer is actually there. I have a memory of answering something like ten of fifteen questions in the test time in Grade 9, and out of around 30 that wrote the Junior one in the school that year, I placed first. The one that placed second was in Grade 10, and the one that placed third was in Grade 11. I wrote the Junior test for the next two years that I was eligible and the second time I was top in the region of the province, while I think I remember being in the top 100 in the province in Grade 11. That year, I also wrote the Senior one, and the Grade 13 students saw me and reacted that there went their chance of winning it. Because it was written out answers, it was more difficult, and I told them that I was only trying it to get an idea of what to expect - I didn’t think I would do as well.

I won each of those the three years I wrote them, at least in terms of the school. They weren’t sent away to be marked but rather the teacher handling the Senior Mathematics Contest had the marking guide and scored them with the results the next day, but that meant that I never heard how I ranked beyond the school. Mathematics and Computer Science came easily to me in high school, and it was understood that I was going to the University of Waterloo Faculty of Mathematics. I took a couple Pure Mathematics courses in my first year there, the sort that those going on to Ph.D or D.Math would focus on, and I nearly flunked both of them.

It is a different mindset - Math Olympiad aces likely might do better in areas of physics, engineering, economics or computer science, where the modelling is needed more directly. Just like I didn’t switch to that complex level of mathematics as easily as I had thought I could in light of my high school experience, those taking a path to Masters or Doctoral degrees in mathematics didn’t necessarily switch to the mathematical deciphering of situations that the math contests explored.

“Can”…? John von Neumann passed away over 60 years ago, two years before the very first International Math Olympiad was held.

The problems of that first IMO, back in 1959, would be solved quickly not just by von Neumann but by virtually all present-day IMO contestants. “No time” is a bit of a stretch: the geometry problems (4, 5 and 6) require at least a bit of mental diagramming and angle chasing. But they are not a serious challenge to trained students today, and they would not have been any sort of challenge to von Neumann. He was a frightfully powerful and fast problem solver. He’d be bored.

Present-day IMO is a different matter. We can’t say for sure, of course, and it’s easy to ascribe god-like powers to von Neumann, but I don’t think he would see right through P3’s and P6’s of recent IMOs “in no time”. Even P2’s and P5’s may get him to think for a few minutes. Some very tricky problems – I can idly speculate which – he’d shatter in seconds, seeing through their core immediately. But it’s unreasonable to assume that he’d do that with all modern problems.

Math Olympiad problems developed a style and numerous techniques and methodologies over the years. von Neumann could do without today’s training camps, but 60 years of cumulative evolution are not nothing, even for his extraordinary mind.

If he were alive today and somehow cared about math Olympiad problems, he could quickly become a world class Olympiad problem solver after a few weeks of catching up. Many IMO problems are a walk in the park for several other professional mathematicians (not all of them!), and he’d probably be much faster than all or most of them.

Common? Very few school kids even try to solve any IMO problem, so no, it’s not common.

If you’re looking for affirmation that you did something special, I’m afraid I can’t say. Of the people who look at IMO problems without studying Olympiad-style problem solving, a lot more walk away thinking they’ve solved something than actually solving something.

If you’ve correctly solved IMO 2024 P1 and P5 and IMO 2017 P1 and P5 (I don’t know what you mean by “etc”), that’s great. If problem solving interests you, spend time studying the methodologies and solve as many problems as you can; that’ll be more fruitful than checking if what you did is common or uncommon.

(…)

The answer is that most of the domestic USA IMO people that I know have not found MIT math classes to be e.g. extremely difficult to get an A in, and with some amount of work most IMO medalists do pretty well. If you have the mathematical maturity, the problem solving ability, and the relevant background for a class, you should learn the material and get a high grade.

That being said, certain classes like 18.785 are a lot of work for everyone (and you learn a lot!). Also I have heard of more cases of international IMO people struggling with MIT math classes, as in other countries perhaps it is more likely that someone could do well on the IMO but not really have a strong math background in the traditional sense.

Someone spoke here as a non-IMO medalist. So here’s mine as a Bronze medalist of IMO.

The answer depends on the exact college you are talking about. For an average college, you shouldn’t make the comparison at all: An average math major at the end of college (or even during his/her second degree) is far behind an IMO medalist even at the beginning of college.

There’s one litmus test for this: the ability to write proofs. Every IMO medalist knows how to write proofs, even if their proofs are not very rigorous. At the other hand, most majors in an average college do not have the ability to do proofs. Many of them (as far as I see) even fail to write down a double integral as a solution of a problem.

Without the ability to write proof you’re not even at the door of Mathematics.

Of course, if you’re talking about the best universities, that’s another story. The math in research is very different from the math in competitions anyway.

Anyway, for the OP: If you’re really interested in Mathematics, then don’t be scared. Spend some time (i.e. months) to learn how to do proofs, and once you get used to proofs you’re on par with IMO medalists. You need to go through some painful transition on how to do Mathematics though.

I think the skill required for math competitions is a subset of the skill required for successful math research.

Math competitions is about problem solving under time pressure. Moreover, the problems are special. You know an IMO problem has a solution that is usually based on one clever idea and fits within a few pages.

In math research, the first step is establishing a research program. This involves a long term vision that seems to be unrelated to math competitions. There will be larger and smaller projects. You face problems for which you do not know the existence of any type of solution beforehand. It is important to see the big picture, beyond a small clever idea that fits in a couple of pages. It is also important to have perseverance through a prolonged period of time.

In the context of a larger project, you usually encounter smaller sub-problems in the style of IMO problems. This is usually in the form of proving lemmas. Math competitions skill comes handy there, because you need to solve them in order to move forward. Pretty much every important mathematical result involves at least one step that is tricky to figure out.

In math research, it is also important to collaborate effectively with your colleagues.

As you can see, there is more involved in math research compared to math competitions. There are also several very successful mathematicians out there who are not as good at problem solving as you would think, but collaborate effectively with other mathematicians and contribute other parts of the puzzle.

IMO math isn’t that much higher than the level of math you learn in high school; the only major difference lies in how you are expected to apply the knowledge you have.

At the IMO, there are four fields of mathematics that are covered. These are, as follows: Combinatorics, Number Theory, Geometry and Algebra. Of these, the only formulae or theorems you might need that are not taught at high school are some of the more complex theorems in geometry - although you should be able to solve most IMO geometry problems with basic methods, the true difficulty lies in how you choose to use the method - and some of the concepts used in algebra and number theory, such as modular arithmetic.

Most high-schoolers would have no problem understanding the solutions to IMO problems. Solving the problem yourself, however, is a whole other ball game. Typical high school or university math exams generally ask questions where the theorems or formulae you need to use are quite clear, and the challenge comes from remembering the right formula and not making a calculation error. With IMO problems, you are thrown headfirst into the pool - you have no clue which theorem to use, which idea to apply, and you simply have to figure out a path to your solution. There are many such paths, some more elegant than others, and it is for that reason I liken Olympiad problems to exploratory journeys - you never know if you’re going in the right direction until you reach your destination. Normal math, on the other hand, is a race down a straight road, with the major constraint being time. There’s no lack of time at an IMO - you have 4.5 hours for 3 problems!

I don’t think so.

Most people solve Rubik's cube by looking up other people's solutions, then they spend time practicing to do it as quickly as possible. A few just pick up the cube and work out what they have to do to solve it, then they put it down and look for a new challenge. Solving olympiad problems are the same.

The olympiad problems posed at a lower level tend to use well known tricks. It is very hard to think of truely original problems requiring new methods involving only high school maths. If you spend enough time going over past problems looking at other peoples solutions to learn the tricks you will be able to do those problems.

At the level of the IMO it is different. They select the problems from many international submissions made by top mathematicians and they are looking for problems that can only be solved with clever new ideas that are different from those used before. If you want to be able to solve them then you can practice by doing past IMO problems but you must never look at other peoples solutions until you have found one of your own. If you cant solve one problem now then leave it and come back to it again later. The techniques for finding new ways to solve problems can also be learnt, but not by looking at other people's solutions because the route they took to find the solution is not written down.

There is some overlap, but in my opinion the skills are different. Obviously there are some people like Terry Tao who have done brilliantly at both.

Solving IMO problems is like solving undergraduate mathematics problems, only harder. Some other mathematician has already devised and solved the problem, and verified that it can be solved in half an hour or so, no matter how much ingenuity you may need to do so.

Solving real research problems is different- once you are a mature researcher you have to devise your own problems to solve. You must triage possible research problems, disregarding problems that are too easy or too difficult for you. You might never manage to find a solution to some innocuous sounding problem.

In my long career as an applied mathematician and as a learner and teacher of mathematics I have known plenty of brilliant undergraduate students who did well in examinations and mathematics competitions and who went on to be research students at prestigious universities around the world, but turned out not to have the ability to be self directed pure mathematics researchers. On the other hand, I have known plenty of competent but not apparently brilliant students who later did brilliantly at research.

What are my qualifications for having an opinion on this? I have had a successful career in research as an applied mathematician. As a teenager I came third in Queensland in the senior section of a mathematics competition for high school students.

The young man who won the mathematics competition in my year went on to top the matriculation examination in Queensland, and get an undergraduate scholarship to the Australian National University, where he got straight High Distinctions and a first class honours degree. At that stage on paper he had probably the best academic record of any ANU graduate ever.

He got a scholarship to Oxbridge, where he enrolled in but didn’t finish his PhD. He later returned to Australia and finished a less theoretical PhD in economics, and worked for the World Bank based in the USA. He got a high up job in the Australian civil service. In his forties he finally got a three year research job in a university, and after a few months said to me, “This research business is a lot more difficult than I thought it would be”. He was and is a very smart guy, but just didn’t have the ability to imagine and then solve suitable original research problems.

I went to the IMO quite a long time ago, in 1996. Let me try to describe what I recall from my experience, 18 years later.

• The math: even though I did pretty bad (I got a grand total of 6 points!), I still learned a lot, and I could fully understand the solutions to the problems after the test. I am proud to say that I got the same score in problem 5 as all the Chinese team combined: 0 point. Joking aside, I still got to learn a lot from the test and from other contestants (I vividly remember a guy from Armenia teaching me how to solve that problem 5!).
• The place: IMO 1996 was in Mumbai, India, and I am Brazilian (even though my middle and last names announces my Asian heritage, I was born and raised in Brazil). So it was an incredible experience, especially in terms of culture shock. I learned to respect other cultures; I learned that there are nice people everywhere; I learned to respect my own country.
• The people: I think that's the main reason IMO is so cool. You have the opportunity to meet people from all over the world. I remember making friends from Albania, Switzerland, Argentina, Colombia, Portugal, Morocco, Armenia (we played soccer with them, the grass was so tall that we could barely see the ball) and so on. Everyone is bound by a common interest, so socializing is easier right off the bat. And of course, there are my teammates, which I consider friends for life. I still get in touch with 3 out of 4 of them (maybe I'll meet the 4th one again, we even shared a room and became best friends!).
• Excursions: we went to Pune climb a mountain (we were supposed to see a temple, but we lost our way and saw... a TV tower.) and to an amusement park. We were free to walk around town with our guide in our free time too; I remember getting into a cab, going to the mall and seeing a snake charmer.

Interestingly, the least I remember from my IMO was the tests. I mean, I do remember the problems, but I can't remember how I reacted to them. Again, I was never very competitive to begin with.
I still go to IMOs as a team leader or coordinator, and I still think it's fun. But mainly because of people. It's a great party with lots of fun stories.
In retrospect, maybe I'm not the best person to describe this; I'm not competitive enough.