Hi. Both of those great competitions for high school are upcoming, so this may be a good time to discuss about them and probably make some comparisons.

Firstly, some backstory of my experiences (if you will get bored you can jump to next paragraph :P). When I was in high school I was definitely much more mathematician than algorithmist, I was doing math for my whole life but started algorithmics in high school. I considered algo as a very interesting field and devoted it much time, but math was for me more important and I was simply better at it. I took top spots in math contests when I couldn't perform well in any algorithmic contest (it was a very often case for me that I solved problem, but received very little points, because of some bugs, because in POI there was very little feedback). In my last year in high school I managed to qualify to the IMO (it would have been a tragedy for me if I wouldn't have make it) and also to the IOI, which was a big surprise for me. At IMO I did very well in 1st day, but on 2nd day I messed some cases in one problem and got completely stuck in a geometry problem for sth like 3h. Up to high school, I think that I devoted more time to geometry alone than to algorithmics and couldn't solve problem, which was solved by ~100 other contestants. I was really confident about my math skills and I got an impression like I'm surrounded by loads of really outstanding geniuses (not to mention Teodor Von Burg and Jeck Lim :) ). In final result, despite my really good performance on 1st day, I got 25 pts, 64th place and silver medal. In IOI I solved 3 problems and I considered them as really easy, thought that I didn't really do anything smart and even more, I messed up bruteforces to problems on 2nd day, because of some childish problems, which could be solved in a second using valgrind/gdb. I got an impression like there were few smart guys on IOI, but most of those people didn't know really basic stuff. In result I got 360pts, 28th place and silver medal, which was in fact significantly better position than that in IMO, because 28 is much less than 64 and I was just 4/600pts short from gold medal. So comparison of those performances is somehow weird. I was significantly better in math than in algo, on IMO performed rather well (beside receiving 3/7 because of not being careful in functional equation, but that is another long story :P), got stuck on hard problems only and took not that good place, while on IOI I performed not really well, got really stupid bugs, but took much better place. (By the way that is really something weird, but you can go to results of IOI 2012 and find some really outstanding guys, who got really small amount of points, for problem "Rings" which seemed quite easy :P).

As a conclusion, this might cause some negative feedback, since this is algo site not a math one, but I consider IMO as a much bigger deal than IOI and gold medal on IMO as a significantly bigger achievement than gold medal on IOI. Comparing to CF rating system I think that "rating cut-offs" for IOI medals would be something like 1500/1750/2000, while at IMO it would be something like 1700/2000/2300 if we will treat this as a corresponding math skills to algo skills of people with these ratings. Moreover, on IMO there are often some extremely hard problems, and they are always solved by 10-20 people, while in IOI there are some definitely easier problems which are solved by ~6 people (check Last Supper from IOI 2012). One reason of that is that on IOI you also have to code your solution without a single mistake, but either way it is still a big difference. If you're disagreeing with me (or agreeing :) ) I invite you to explain your opinion.

By the way this feeling (in short that IMO >> IOI) was strenghtened by organisations of those events. IMO organisation was really great, we were placed in a really luxury hotel and there were many events like tournaments in a football, table-tennis and many many more, there was a recreation hall where there was a big amount of things to do, karaoke, many games, video games, drums and much more, it is hard to describe how this place was awesome, in short recreation hall = delight overload (and what is most important, I was very surprised by presence of my favorite video game — Pump It Up, you can see me playing here https://fbcdn-sphotos-e-a.akamaihd.net/hphotos-ak-xap1/t1.0-9/46120_4940025175001_299353650_n.jpg :D) and IOI organisation was the exact opposite. There were 2 good things on IOI — problems (which is of course the most important thing) and food, but everything else was really bad. There were very little activities we can do, and we were really often forced to wait for an Hour for nothing. Organizers even managed to make a trip to Venice a horrible one, which is a really hard achievement.

Talking about organization from host, it actually depends on the host country. IOI in Thailand was very gorgeous. Similarly I think IMO contestants can come up with example where it was not that gorgeous (something like IOI in Italy).

Hmmm, I guess you're right. I know (not from my own experience of course :P) that IMO in Kazakhstan was a total failure. But that comparison (Argentina vs Italy) just strenghtened even more my biased opinion :P. By the way, on the opposite, there are some math competitions for students like IMC, but in my opinion they are not that prestigious as IMO, ACM ICPC is bigger deal than IMC :). And actually I'm doing much more algorithmics than math :P.

I have heard, that some participants were awarded by notebooks in Kazakhstan, which is much more cooler, than in other IMO's(nothing)

Yes, that is true, but this was the only good thing on whole IMO as far as I know :P.

That's still cool though.

Yes, it depends on the country. I've been in several IOI's, and here is some comparison:

Concluding from your post I was really not lucky in "choosing" my IOI :D. By the way being on 7 IOIs is impressive. Were you a contestant in 2005 and 2006 and (deputy) leader in next years?

Yes, it's easier to get to several IOI's as a leader...

I wonder what tourist would say to that :D

Format for mathematical problems in IMO is very different. For example, tourist got last gold at IMC(which is almost IMO for Universities in Europe) and couldn't solve Problem 7 which would be 2nd easiest problem in IMO from 6 problems. But this particular problem is proof based which is not familiar for IOI participants.

If you are good at math, it doesn't mean you are good at programming, it just means you'll understand some algorithmes and ideas faster and (maybe, not necessary) solve combinatoric problems better. I started doing programming at last school year, when I have understood, that my life will definitely not connected with math. "while at IMO it would be something like 1700/2000/2300" — that sounds funny, because my results were better, than this scheme proposes:) Actually, IMO isn't very objective way to graduate mathematical abilities. I tried to solve problems of different IMO's and my hypothetical results were very different. At one year you must be good at Number Theory and Combinatorics for getting a high medal, at the other year it's enough to be good at Algebra and calculating geometry. So, I find connection between IMO results and IOI results isnt very strong. Surely, programming requires more expirience, working, not a big talent. CodeForces problems often require some combinatorical skills, but it isn't the same as great mathematical skills:)

Lol, why do you minusing it? If somebody has some contra-arguments, I'd like to see them.

People just downvote non-red comments on here for fun... Don't take it personally.

Thanks for your support)))

No Problem ! It happens to me all the time too ! ... I bet someone will come and downvote these comments as well. lol :P

I don't know what are you talking about IOI 2012 organization. Trip to Italy was one of the best in my life, there was no moment when it was boring to me. Trip to Venice was really a bit failed, but you could find a way to make it more interesting for yourself. And the food was great, the food was really great!

Yes, the trip to Venice spawned some catchphrases, such as:

Also, (roughly) a conversation of one of our leaders with an organizer lady:

followed by Slovak leaders and contestants making our own trip to Venice, the main advantage of which was: we had to pay for the lunch, but:

Achievement "eat true Italian pizza in Italy" complete!

We did have to pay for lunch, but we waited for it 10 minutes, not "10 minutes".

Anyone remembers the sample task called "Italian Queue"? :)

Agree with you. Some people just think that organizing an excursion for 600 guests to the one of the most popular places in the world is as difficult as to the Russian village.

I also think that IMO is more difficult than IOI. I would say that IMO bronze equals IOI silver, and IMO silver equals IOI gold.

Also: if you are a good IMO contestant, you can become a good IOI contestant as well after some training, but this doesn't work in the other direction.

You'd be surprised how far trig/coord-bashing all geometry, learning number theory by reading Niven/Zuckerman, and doing a bunch of algebra problems get you in math contests...

The number quoted to me by CHN IMO contestants was about 900 'unique' problems in OM, which seems comparable to the syllabus of modern OI.

Nope. Unless by "far" you mean "solve problems 1 and 4".

Any but these problems are usually made to need insight for a working solution, and can rarely be solved by bashing. There are insight-problems in informatics contests, but they're pretty rare.

The main difference between IOI and IMO is that IMO doesn't have subtasks, and doesn't care about anything like that. In IMO, you need to correctly solve the given problem, or at least get as close to it as possible. In IOI, you have other choices: solve a special case of the given problem, or write a bruteforce or semi-bruteforce by utilizing one property that leads to a solution, but not several others. In IMO, it's very likely that this property would only give you a point, because it's just a random observation, or it could be so trivial that you won't even get that point.

IMO really expects math to be like a puzzle which you need to build, then they lift it up by one corner and you're given points based on how many pieces don't break off from it just by lifting it. If you build 2 disconnected components, you just have bad luck :D

I haven't followed IMO for a few years, but my impression is that at least half of 2, 3, 5, and 6 are still geometry / number theory / algebra?

With computer aid, most OM geometry / algebra questions can be solved fairly systematically using tools like mathematica / MATLAB. So it's more of a question of whether the contestants want to bash, and the track record from geometry #3/#6s seem to indicate yes.

Number theory is a bit of a exception (in that there are specific knowledge that help), but there is a quite large literature that one can dig. Combinatorics is the only real exception I suppose.

I don't think the IOI subtasks affect the competition at the highest levels: most contestants in that bracket get them anyways. It's more of a mechanism to allow problem setters to introduce more interesting problems, instead of allocating entire slots for easy problems.

Yeah, well, there are generally 4 main topics of IMO problems (they can overlap, of course). Algebra, combinatorics, geometry, number theory. In lexicographical order :D

Do you realize that behind an online tool's computation process, there can be one simple theorem or several numerically hard steps? It can be possible to bash that, but not within the 5 competition hours. Example: a nice integral (not an IMO-style problem, calculus homework).

Pure hard number theory seems scarce at IMO, I get the impression that combinatorics or algebra (in integers/rationals) is often IMO's number theory, or sometimes it's just about observing divisibilities, which isn't really like informatics' math problems. And pure combinatorics is pure insight.

Algebra can be bashable if you get lucky (calculus is often a good thing), but again, it can turn out to be so ugly that knowing a useful inequality (such as Cauchy-Schwarz applications) can help a lot.

Geometry... that's not really my cup of tea, but I'm probably regarded as someone who can bash geometry well (I don't know advanced synthetic geometry and I'm too lazy to learn it, so I can only bash), and I failed to solve last year's problem 3 analytically. Generally, it doesn't work out well for me with harder IMO geometry, so it's not surprising that I consider it pretty much unbashable (you might be right here, but I just don't see it based on my experience).

At least when using programming tricks. I solved a nice problem recently: given 2 non-intersecting planar graphs (drawn in a plane), draw a line between one vertex of one graph and one vertex of the other that doesn't intersect the input graphs in any other points. I suppose an exact solution would do something with convex hulls (which is not really an IMO geometry topic), but I just chose 1 vertex

vat random, found the closest point to it in the other graph, it's on an edge so pick one of that edge's endpoints asv, repeat until necessary. The 2 vertices (vand newv) converge to a correct solution quickly (5 iterations in worst case). That's what programming tools in geometry mean to me. In IMO, I'd have to prove that it converges with blablabla or try a completely different approach.I often bashed problems (mainly algebra and geometry) after or with some reductions, mixing bashing and insight or needing to solve subproblems. It's possible, but it's certainly not a good idea to try solving geometry 6 by raw systems of equations based on sine/cosine laws.

If we only wanted to focus on the top contestants, then at IOI and IMO alike, the simple problems (last year's IOI had 3) are solved by pretty much all of them. If you look at last year's Wombats, its subtasks defined the top places, almost nobody had more than 55 points (which might be also due to the testing fail, but let's not get into that). Game is the more interesting one: there were many high scoring solutions, and the subtasks actually mattered, because they went bruteforce -> interval tree -> 2D interval tree -> (breakpoint from textbook algorithms) 2D compressed interval tree -> non-asymptotic improvements. There were many solutions which only got to one in this sequence of ideas, which mixed up the results well. In IMO, I imagine you'd only get 1 point for (disclaimer: yes, it's a weird analogy) mentioning interval trees and maybe 2 points for 2D, but not more, since it's just a basic idea and not the point of the problem, but in IOI, it's 2/3 of all points. (Problems like Art are total wildcards, I don't want to talk about that...)

If we went a bit more down the ranklist, Dreaming has interesting subtasks that start to matter. The full solution is basically a combination of 2 separate ideas, and each of them is enough to solve one non-bruteforce subtask (plus, there's 1 subtask that you can get points for if you have the ideas, but your implementation sucks); together, they're enough to solve the last one. And for a lot of points. Similarly, Robots has a subtask that you can solve just by solving a special case: the "1D" version of the whole problem, but that doesn't have many points alotted.

And if we look at IOI 2012, you'll notice that there are very few full scores below gold medalists: nobody below 53rd place (middle silver) got 2 full scores and 54th place was even attained without completely solving a single problem. Compare that to 2013, where the numbers are 142 and 98 (lower and upper bronze, respectively). It changes from year to year (IOI 2011 with 4 full scores not being enough for gold is a great example), but the last 2 years show that subtasks suddenly started to matter a lot (2012) and then a bit less, but still observably (2013).

Sorry for possible mistakes, I just (tl;dr)'d myself :D

"but my impression is that at least half of 2, 3, 5, and 6 are still geometry / number theory / algebra?" — ummm, yes, but what do you expect, poems :P?

With computer aid, most OM geometry / algebra questions can be solved fairly systematically using tools like mathematica / MATLAB. So it's more of a question of whether the contestants want to bash, and the track record from geometry #3/#6s seem to indicate yes." — I will definitely disagree on that one. It is true that many geometrical problems can be solved by computer, but analytic computations are usually that awful, that human don't have slightest chance at succeeding within contest's time. I did ~2 geometries on contests using trig, but 0 using complex numbers and coordinate system (though I'm a bad counterexample cause I enjoyed synthetic solutions) and I think that this is far too big generalization to say "every geo on contest could be solved by bashing". In number theory there is some stuff to learn, but is that a bad thing? You won't perform well at algorithmic contest if you won't know basic dp's, KMP and DFS, that is analogous.

And regarding to what pllk said: "Also: if you are a good IMO contestant, you can become a good IOI contestant as well after some training, but this doesn't work in the other direction." — I think that in many cases it is true. I know many contestants which are starting in contests, because they firstly started programming and then heard about contests. Some of them are smart and they can succeed, but that is not always the case. And math olympiad contestants are pretty always participating in them, because they like thinking creatively.

What I wanted to say is that it is easier to become a coder for a smart person than to become a smart person for a coder ("smart" here means "creative and able to deal with many olympiad problems").

Btw Xellos, you just got an achievement "Write more than Swistakk", that is a hard one to get :P.

One could always try Lorem Ipsum, you know :D

I disagree this one "Also: if you are a good IMO contestant, you can become a good IOI contestant as well after some training, but this doesn't work in the other direction."

Omer Cerrahoglu tried this year to qualify to IOI after training whole year only for this. He failed to qualify for some reason (and sadly he missed IMO selection camps to go to IOI ones). Whilst being good at math certainly helps, having "some training" does not guarantee you'll do well at informatics as well.

Nobody said there's a guarantee...

I didn't know that Omer is also doing algorithmics :O! I was very surprised that he is not going to IMO this year and now I know the reason. I think that this doesn't have to be a counterexample. One year may be not enough to become a good IOI contestant. You probably know better than me, but I suspect that he was probably good at coming up with solutions, but lacked needed experience in coding. In high school I disregarded coding, very often solved problems and not code them afterwards. Learning coding doesn't demand much talent and creativity, but a hard work and experience.

Well, I misunderstood that phrase then. I got it as "if you're good at IMO, there's a high probability to get good at IOI after some practice". I just wanted to point that even if math skills help, there's a lot more needed for be successful at IOI.

Yep, from what I've heard Omer was probably best contestant if only getting correct ideas would matter. Definitely coding stopped him, but I'm pretty sure he practiced that part as well.

I've heard many say IMO >> IOI in difficulties, so this is a good opportunity to give my take on it:

The case with IOI12 supper is reflected in IMO09#6 or IMO96#5: just because the solution to a problem is easy, it doesn't mean it's easy to come up with (I've heard that if IMO09#6 was given as a #1, it would have been solved like a #1).

With math contests, there isn't the equivalent of TC/CF, so what seems to be a hard problem in one part of the world is often 'well known' in another part. This exists in OI as well, but the rotation of TC/CF authors goes a long way towards fix that :-).

About problems of the hardest difficulty: IOI had problems with provable solutions, but no full scores (08 Pyramid Base, 09 Archery), although I consider 03 Code and the O(logn) version of 11 Elephants to be much better (and more fair). These problems feel different than OM problems in that even after good insights, there still remain steps with significant technical sophistication (fairly similar to algorithmic research now that I think about it). From what I'm aware of, IMO usually stay away from this deep end of the difficulty spectrum (ones that come close are 06#6, 07#3, and 07#6).

About organization: both IOI/IMO depend heavily on the organizing country and their budget. The IOIs that I've been to varied significantly, as some of the other posts point out. Aside from having one organizer (kind of like ICPC, but then you get another kind of mess....), there doesn't seem much that one can do about this...

So we have more PIU fans in here :)

This is a video of my teammate Gabaum playing during our visit to Poland for 2012 ICPC: http://www.youtube.com/watch?v=oCZ5T13lfNA

Wow :D. That comment may be a little offtop, but is really great to know that there are more PIU fans among coders :D.

I see that Gabaum is really great :O! I'm at most "blue dancer" when compared to him :P. I'm playing games on difficulties 11-14 (and of course on one dance pad, not two like him :P) and I think that my best performance was to get 2 misses only on a Dignity 12 :P. Though on IMO, as you can see, there was no rail, which is crucial for me and dance pad was sometimes sliding on a floor, so I played levels ~7, but Turkey March 7 was still sufficient to gather audience of ~10 people congratulating me after game :D.

By the way you were playing on my favorite dance pad (because currently the only one in Warsaw :P), but in that film I saw that Gabaum got an occassion to get to know some of its "features" like aborting holds :D.

I'd be happy to weigh in with the opposite opinion. I personally think that OI is in general as hard or harder than OM in terms of the imagination and creative thought required to succeed.

Most of the top contestants in USACO participate in math contests on the side, and many top USAMO contestants do the same for computing contests. I've found that these skills are easily transferable in both directions -- math contestants that begin to pick up CS improve very quickly, and CS contestants that try out math competitions do quite well without too much work. I personally did OI throughout high school and would consider it my main focus for the past few years. This year, I qualified for the IMO (much to my surprise!) AstroConjecture also qualified for both IOI and IMO from the US, and ecnerwala, another IOI team member, placed in the top 12 on the USAMO. stevenkplus solved the hardest problem of the US IMO team selection test in 2012 with an elegant solution completely different from the one the other 3-4 solvers found. Most if not all of us have spent much more effort on CS than math, and I personally felt that my training in CS has helped me with more than a few tough math problems.

As for the claims that OI contests are more technically oriented and less creativity oriented than OM contests, I would say that the opposite is in fact true. Geometry and number theory, from my experience, are quite reliant on the knowledge of various theorems and configurations. Most problems in OI are closer to combinatorics, which is the most creative and innovative of the OM subjects and my personal favorite (though I might be a bit biased here :P). Even the more standard subjects of OI, such as strings or data structures, feel more creative and thought-based to me than functional equations or geometric configurations.

Many OI problems rely on a single insight that is simple but tricky. This might lead one to think that they are relatively easier than problems that require a series of more straightforward observations, but I've found that the hardest and most beautiful problems I've encountered in any subject have been the ones that require a single observation that is easy to explain but extremely difficult to find.

As a side note, the IOIs I've been to were all excellent, though that may just have been me getting lucky, as the two IOIs I've competed in so far were in Italy and Australia. :)

Thanks for interesting point of view:)

I think that different people have their brains working in different ways — even if they are pretty good in OI and OM at the same time. And that is why someone prefer OI and someone prefer OM. You said about

single observation that is easy to explain but extremely difficult to find— and for me most often it looks likemuch easier to find than to explain— thinkingit might somehow work, because such magic often works. That is why i do not think that i'll have any chances in OM and that's why OM seems harder for me.Wait, in which competition? "Reliant on knowledge" would indicate that you're arguing one of them (so OM from the context) being technically oriented, but the argument I'm expecting from "the opposite is true" is not "OM isn't completely creativity oriented, you need knowledge too, and similarly you need insight in OI sometimes" (which is what I'm understanding as your argument here), but "OM is more technically oriented than OI", and I don't see it anywhere...

In informatics, yes, but the IOI syllabus abhors math, even simple things like modular inverse — last year, an algorithm for GCD was provided! But the "combinatorics" topic in OM seems to depend from person to person: me and Baklazan are both coders at roughly the same level who can solve combinatorics problems in informatics quite well (similar skillz), but he's really good at OM combinatorics, while I'm horrible at it :D

Yes, algorithms are often very creativity-based when you're making them from scratch, but they're usually learned beforehand with all their implementation perks and IOI often expects you (at least to solve some subtasks, like 1-3 in last year's Game) to implement, not discover them. This has gotten to the point where IOI problems need creativity or there'd be too many full scores in the top places (or people would start failing on implementation details, which'd be horrible). Still, IMO problems seem to me that they require creativity much, much more and from a far wider range of topics.

"This year, I qualified for the IMO"

Where are you scott_wu? http://www.imo-official.org/year_reg_team.aspx?year=2014&code=USA

Good question. :)

I actually turned down IMO this year despite having the opportunity to go for a few reasons. I was excited to start work at Addepar, and I felt that having both IOI and IMO in my schedule would make for a really busy summer -- I'd be in training camps from May to the start of July, and I'd have the two contests back-to-back right after that.

As a former IMO and current IOI contestant, I have also gotten the feeling that IMO is more of a "big deal" than IOI. But the primary reasons I would attribute it to are just a combination of historical accident and societal influence, rather than any intrinsic qualities of the subjects themselves. Nobody seems to have mentioned this yet:

three decades— there's much more time for former contestants to spread the word, for discussion groups and support networks and training camps to be built, for people to discuss the most effective ways of training students for it, for mock tests and sample problems and educational materials to be written, etc.I don't really have a strong opinion on the relative difficulty of the two contests. I will say I think the IMO tests a wider range of topics than the IOI, with four subject areas that overlap somewhat rarely, all of which contestants have to grasp to be successful. The algorithmic ideas of IOI seem to be more interrelated and focused.

It stands to popularize competitive algorithmic programming not just on sites like CF (because I doubt a vast majority of students would even care to try something random on the net), but separate effort on country-wise (or smaller) levels. Yes, I have in mind correspondence seminars, which are quite strong in Slovakia — the programming one, KSP, basically creates Slovak informatics olympists (and olympi**cs**), and considering how well Slovakia fares in IOI relative to its size, you can see the effectiveness. It just stand on people to make their own effort, and at least some cooperation with schools, to make this effort known, and I think it could do wonders occasionally :D

Image link broken. Aww, and I wanted to see you playing Pump It too... :(

Me too :(