I agree very heavily with the sentiment of "many competitions are too hard"
One thing that is definitely true is the math competitions are too beginner unfriendly nowadays. Back in 2008, one could score reasonably well on AMC 12 (like 90's or 80') with little interest or preparation before hand (I mean reasonably well in relative terms to preparation time). This could be encouraging to some who might not have been interested in self studying math before - they could say " hey, I almost qualified for the AIME, a national competition, maybe if I put in some effort, I really could next year". Nowadays, the AMC's are pretty discouraging to beginners. Unless you've been doing competitions for years and mastered the previous level (say Mathcounts State or Nationals), the AMC 10 and 12 will feel unnecessarily hard (to do well in).
I agree it seems very lopsided for each competition to serve the needs of only the top 1% of people taking it, while draining confidence, or being unhelpfully hard, to 90 % of people taking it.
Considering the time restraints of competitions, most competitions can differentiate the top 10 with the majority of hard problems replaced by easy and medium problems.
Another thing is that many beginners don't understand the relative difficulties of competitions. A local Alabama math competition is generally going to be miles easier than HMMT Feb. But a true beginner who doesn't know the difference might treat their results at both competitions similarly. It takes a lot of confidence and experience, built from previous successes at easier competitions, to take an HMMT test and not feel bad at getting 1 out of 10 problems correct (or at least to understand that the score is more an indicator of the difficulty of the competition than one's personal abilities).
I think there is a big and growing educational divide. Some people grow up with access to great tutors or programs, or learn to be self sufficient in learning from a young age. Others grow up in environments that are not conducive to learning math in depth. It is hard to serve the needs of everyone, since the people who are well off tend to race ahead in terms of learning and experience, while those not so well off (financially, socially, culturally) tend to fall further and further behind.
But contests should be more inclusive. Math education should be a level playing field for everyone. While not everyone can make it to the IMO, the first stage of selection for US IMO team should not feel unnecessarily brutal. A good math education should decrease the gap with the rich and poor, or at least level the playing field.
But nowadays, doing well on prestigious math competitions seems only feasible for those whose parents can afford to send them to high quality training programs or camps that teach math and math competition well, while those whose parents cannot afford such things are left in the dust (much more so than 10 years ago).
So the well-off get more educated, while the poor remain left behind.
alright, last night i was actually in the middle of a run while i got this comment LOL so i didn't give the most substantive reply, so
> One thing that is definitely true is the math competitions are too beginner unfriendly nowadays. Back in 2008, one could score reasonably well on AMC 12 (like 90's or 80') with little interest or preparation before hand (I mean reasonably well in relative terms to preparation time). This could be encouraging to some who might not have been interested in self studying math before - they could say " hey, I almost qualified for the AIME, a national competition, maybe if I put in some effort, I really could next year". Nowadays, the AMC's are pretty discouraging to beginners. Unless you've been doing competitions for years and mastered the previous level (say Mathcounts State or Nationals), the AMC 10 and 12 will feel unnecessarily hard (to do well in).
yeah, it definitely feels like the barrier to entry has increased by a large amount -- because "serious" competitors have started spending more and more time and money on preparation, it seems like the AMC has raised its difficulty standards in response. unfortunately this had the obvious consequence of making the contest far less approachable.
one idea i'm thinking about currently: the AMC has this idea where the top 2.5% / 5% of competitors qualify for the AIME. i wonder if it might be better to just ... you know, make the contest *more* inclusive? like, instead of constantly raising the difficulty to make sure that 110/120 is a "top score", let people get better and better while keeping the contest the same difficulty such that the top 2.5% / 5% of people are now getting 130, even 140 -- but instead of making a cutoff based on percentile, why not just let people above a certain score qualify for AIME, with no change to the USA(J)MO qualification rules?
this way people who are talented and have potential in math are more likely to qualify because instead of having to *beat* a bunch of people who're studying their asses off, they just need to demonstrate that they possess significant enough aptitude to get close to / exceed a cutoff. like i don't think it makes sense for the AMC to limit to a *percentile* of people; it should just be based on who has enough ability, which doesn't have anything to do with percentiles. (the person whose walking ability is in the 40% percentile nationwide is still going to be able to walk a few miles without falling down!)
> Considering the time restraints of competitions, most competitions can differentiate the top 10 with the majority of hard problems replaced by easy and medium problems.
exactly!
>A local Alabama math competition is generally going to be miles easier than HMMT Feb. But a true beginner who doesn't know the difference might treat their results at both competitions similarly. It takes a lot of confidence and experience, built from previous successes at easier competitions, to take an HMMT test and not feel bad at getting 1 out of 10 problems correct (or at least to understand that the score is more an indicator of the difficulty of the competition than one's personal abilities).
i think this is a really important point: i know one of my friends, when she took HMMT, actually found that struggling through all the problems and getting a close to 0 score was a good experience because it showed her how much more she had to learn. but she was from a top-10 team and she'd grown up around people who'd qualified for and won olympiads, whereas our hypothetical person from alabama would likely be far more discouraged.
> But contests should be more inclusive. Math education should be a level playing field for everyone. While not everyone can make it to the IMO, the first stage of selection for US IMO team should not feel unnecessarily brutal. A good math education should decrease the gap with the rich and poor, or at least level the playing field.
But nowadays, doing well on prestigious math competitions seems only feasible for those whose parents can afford to send them to high quality training programs or camps that teach math and math competition well, while those whose parents cannot afford such things are left in the dust (much more so than 10 years ago).
So the well-off get more educated, while the poor remain left behind.
I totally agree! From experience, I can say that struggling to solve most of the problems on a competition can be demoralizing and an unhelpful experience.
I thought about one Evan quote saying that generally the reason why not everyone takes the USAMO is because scoring zero is demoralizing and totally unhelpful (as I stated above) and that's why the process is in place - to only have the people who will be able to make progress and enjoy the problems fully actually take the test. Why take a test if you're not going to make any progress? That's just a bad idea.
As someone who also participated in many math competitions when I was younger, it was definitely cool to read about some of these processes and thoughts that went into creating the problems. I wish I enjoyed them as much as you did though, haha. I was one of those kids that wasn't too bad at math, didn't enjoy but didn't hate math competitions either, and got pushed by my parents.
I am not even sure ego is the main issue (responding to a comment later down the thread). At least for collegiate contests my guess is that it's lack of experience and not negligence. e.g. HMMT February problem czars are typically writing the February contest for the first time, are only a few years out of high school.
It's easy to say "we should make sure the contest is accessible". It's hard to actually make the judgment calls of "let's use problem X versus problem Y because X will probably be solved by about 80% of students while Y will be solved by about 50%, even though Y is more elegant". The issue is that, without tons of experience working with students, it's nearly impossible to know what those percentages will be. (I still get these decisions wrong all the time myself, look at JMO 2021.) It's doubly true if you're an IMO multi-medalist for which all the problems feel easy anyways. It's triply true if you are in a situation where you didn't have time to personally solve every single proposal (e.g. IMO jury).
Putnam is the only example I can think of where median scores of zero are a source of pride. Every other contest, the usual response upon seeing the statistics of the exam is "oh crap, we messed up". It's part of what makes contest design so difficult, that even assessing the difficulty of a single problem in isolation is perniciously slippery.
(Also, with regard to JMO 2021 -- I don't know the exam but errors are magnified a lot more on such a short exam; I don't think 6 problems is large enough ... whereas if you have 30 problems to work with I'm *certain* it's possible to make a subset of them quite accessible)
> I am not even sure ego is the main issue (responding to a comment later down the thread). At least for collegiate contests my guess is that it's lack of experience and not negligence. e.g. HMMT February problem czars are typically writing the February contest for the first time, are only a few years out of high school.
I'm not sure I agree that it's lack of experience and not negligence; my reasoning would be that HMMT has this problem ... literally every year, right?
Even if you're only writing / organizing the contest for the first time, you have years' worth of data to work with. At that rate I'd be pretty confused if year after year you still end up with the same problem -- way too many zeroes and low scores. I would attribute this more to negligence at this rate, in the sense that if you're a new problem czar and you're not actively looking to try and make the contest easier you are being negligent, right?
I understand how you feel about problems being hard to judge, but this is why people other than the problem czar themselves exist. The head organizer has a huge pool of people to draw on that aren't all MOP/IMO-level -- surely they can find someone who only qualified for AIME in high school, for example, or even just attempted the AMC and didn't necessarily qualify. I would say that if a problem czar isn't actively trying to include people of all different skill levels in the process of setting a test that this is pretty much negligence *due to* inexperience, but at that point we're arguing semantics ... I suppose I was lucky in this sense because I used my 6th-grade brother as a guinea pig multiple times during the process.
I agree we're arguing semantics :) my point was that to people without much experience working with students, their calibration of student's ability is usually far off, whether they realize it or not (and usually they don't).
In particular, if you want a post like this to be useful advice (rather than merely correct advice, which it is), you'd want to give some concrete suggestion of how to improve calibration. Telling people they suck at something (that they do suck at) is a fine first step but begs the question "how to improve?".
In other words, I would say the _how_ to make problems accessible is much more important that _why_ here (along the lines of your reply). I think it's hard to find an HMMT problem czar who disagrees with not zero-ing out half the kids. They just don't know how to get there.
fair enough :P I admit to not giving the most specific advice of all time, but also, how much *specific* advice is there to give? I think “write easy but interesting problems” isn’t a terrible start, and probably gets you more than half the way there …
I suppose I can add another section detailing random things I also did (?!?) thanks for the advice :P
> Of course, there are other contests where many students don’t solve any problems — perhaps the USAMO is a good example — but the point of the USAMO is not to raise interest in math; anyone taking this exam is a top-500 math student in the nation.
It's not a "good" example in the sense that we think it's also a pretty bad experience to solve no problems on a nine-hour exam. But it's tough when you only get three problems each day.
Is it weird that I feel like the main "problem" in USA based competition is usually the time limit is too low?
I feel like if we allow more time (like even an additional 30 minutes), and probably adding 1-2 more easier problems (which is fair, since we allow more time) for those university contest, it could be a more encouraging experience to the participants.
This is even applicable to AMC, although honestly I'm not really familiar with USA competition scene anymore, but I am pretty sure there was a problem in recent AMC 12 that includes SFFT / telescoping (where I think it's pretty hard to see the pattern) in their first 10 problems (I think SFFT / telescoping of that kind is hard for newer students, since they are not exposed with math competition techniques, newer student tend to play around with patterns and such). While I understand this is to cater people for AIME qualifying purpose (since the skillbar is already higher), but I feel like the difficulty curve could be smaller if we add more time (hence more problems --> better difficulty curve) to accommodate the newer student as well (they could solve more problems as well as they don't feel rushed because of the time limit). An example from my first thought is there could be a 100 minute test - 40 problems.
you have some interesting ideas here -- i think the one major qualm i have with *increasing* the time limit is that higher amounts of time are actually a turnoff. imagine if the AMC were 2 hours instead of 1.25 hours. i think less newer students would want to take it then -- longer contests are more intimidating by their nature.
i think a better idea might be in my reply to Xinke in the comments section -- instead of making a cutoff based on percentiles, just make the cutoff based on ability. that way people aren't just left in the dust when their peers who've been studying for ages qualify for AIME.
i think i'd honestly prefer to reduce the time by 15 minutes, say, and probably cut the contest down to 20 problems (or smth similar like this). i think this would probably lead to an increase in number of participants! but if this were to happen they would really, really need to fix the difficulty curve :P
Fair, I'm not from USA (although I was interested in USA competition scene) so I don't know how the students behave there, but in my country, we are used to longer time limit.
i think that longer time limits are good to support more depth of thinking and less "trick-based" approaches to problems, unfortunately i think this would turn more kids off to the contest : ' (
related anecdote: one of my math-adjacent friends told me that she finally gave up on mathcomps after zeroing pumac (which this year was just ridiculously hard for no reason--even i struggled a *lot*). at the time i found it rather surprising since i attach very little weight to my scores on college contests, but i think there may be a real effect here
yes! this is something which has tangible effects on people -- there's no reason for a strong math student (i do know the person in question -- she qualified for AIME and scored quite above average on it) to get a 0 on a contest like PUMaC
idk if this is supposed to be like new ? this is what i strive for when i write problems anyway (which is why hard problems ive written are very scant; most problems ive gotten into contests are easier)
why are you sectioning the blog post with numbers when you can section it with… section titles… that you already have…
hey i wouldn't have written this if half the contests out there *didn't* do this :| i think there's also a lot more to this than just "write easier problems"; surface-level this is the advice for contest writers but i think it's a lot more about not letting your ego get in the way of effective design, which is a principle applicable to lots of things
and in any case there's nothing wrong with rehashing something important that a lot of people don't pay attention to :)
i told you this elsewhere, but you can check through PUMaC's stats from last year: I skimmed the div B results for algebra and geometry, and in each about 25% of the competitors solved one or less problems. i think this is definitely Not Close to optimal
i mean in this case -- almost AoPS mocks are created for vanity's sake, from what i can tell (oh, i can write a mock? and show off my skills?); HMMT has serious problems; putnam is almost nonsensical in this regard -- i don't know why it's a symbol of pride or smth that so many people get zeroes; ... even some other student-run contests at colleges have the problem that their earlier problems are just not very interesting. I know MMATHS had problems regarding this (and difficulty gradient) in the past so ... /shrug
I agree very heavily with the sentiment of "many competitions are too hard"
One thing that is definitely true is the math competitions are too beginner unfriendly nowadays. Back in 2008, one could score reasonably well on AMC 12 (like 90's or 80') with little interest or preparation before hand (I mean reasonably well in relative terms to preparation time). This could be encouraging to some who might not have been interested in self studying math before - they could say " hey, I almost qualified for the AIME, a national competition, maybe if I put in some effort, I really could next year". Nowadays, the AMC's are pretty discouraging to beginners. Unless you've been doing competitions for years and mastered the previous level (say Mathcounts State or Nationals), the AMC 10 and 12 will feel unnecessarily hard (to do well in).
I agree it seems very lopsided for each competition to serve the needs of only the top 1% of people taking it, while draining confidence, or being unhelpfully hard, to 90 % of people taking it.
Considering the time restraints of competitions, most competitions can differentiate the top 10 with the majority of hard problems replaced by easy and medium problems.
Another thing is that many beginners don't understand the relative difficulties of competitions. A local Alabama math competition is generally going to be miles easier than HMMT Feb. But a true beginner who doesn't know the difference might treat their results at both competitions similarly. It takes a lot of confidence and experience, built from previous successes at easier competitions, to take an HMMT test and not feel bad at getting 1 out of 10 problems correct (or at least to understand that the score is more an indicator of the difficulty of the competition than one's personal abilities).
I think there is a big and growing educational divide. Some people grow up with access to great tutors or programs, or learn to be self sufficient in learning from a young age. Others grow up in environments that are not conducive to learning math in depth. It is hard to serve the needs of everyone, since the people who are well off tend to race ahead in terms of learning and experience, while those not so well off (financially, socially, culturally) tend to fall further and further behind.
But contests should be more inclusive. Math education should be a level playing field for everyone. While not everyone can make it to the IMO, the first stage of selection for US IMO team should not feel unnecessarily brutal. A good math education should decrease the gap with the rich and poor, or at least level the playing field.
But nowadays, doing well on prestigious math competitions seems only feasible for those whose parents can afford to send them to high quality training programs or camps that teach math and math competition well, while those whose parents cannot afford such things are left in the dust (much more so than 10 years ago).
So the well-off get more educated, while the poor remain left behind.
alright, last night i was actually in the middle of a run while i got this comment LOL so i didn't give the most substantive reply, so
> One thing that is definitely true is the math competitions are too beginner unfriendly nowadays. Back in 2008, one could score reasonably well on AMC 12 (like 90's or 80') with little interest or preparation before hand (I mean reasonably well in relative terms to preparation time). This could be encouraging to some who might not have been interested in self studying math before - they could say " hey, I almost qualified for the AIME, a national competition, maybe if I put in some effort, I really could next year". Nowadays, the AMC's are pretty discouraging to beginners. Unless you've been doing competitions for years and mastered the previous level (say Mathcounts State or Nationals), the AMC 10 and 12 will feel unnecessarily hard (to do well in).
yeah, it definitely feels like the barrier to entry has increased by a large amount -- because "serious" competitors have started spending more and more time and money on preparation, it seems like the AMC has raised its difficulty standards in response. unfortunately this had the obvious consequence of making the contest far less approachable.
one idea i'm thinking about currently: the AMC has this idea where the top 2.5% / 5% of competitors qualify for the AIME. i wonder if it might be better to just ... you know, make the contest *more* inclusive? like, instead of constantly raising the difficulty to make sure that 110/120 is a "top score", let people get better and better while keeping the contest the same difficulty such that the top 2.5% / 5% of people are now getting 130, even 140 -- but instead of making a cutoff based on percentile, why not just let people above a certain score qualify for AIME, with no change to the USA(J)MO qualification rules?
this way people who are talented and have potential in math are more likely to qualify because instead of having to *beat* a bunch of people who're studying their asses off, they just need to demonstrate that they possess significant enough aptitude to get close to / exceed a cutoff. like i don't think it makes sense for the AMC to limit to a *percentile* of people; it should just be based on who has enough ability, which doesn't have anything to do with percentiles. (the person whose walking ability is in the 40% percentile nationwide is still going to be able to walk a few miles without falling down!)
> Considering the time restraints of competitions, most competitions can differentiate the top 10 with the majority of hard problems replaced by easy and medium problems.
exactly!
>A local Alabama math competition is generally going to be miles easier than HMMT Feb. But a true beginner who doesn't know the difference might treat their results at both competitions similarly. It takes a lot of confidence and experience, built from previous successes at easier competitions, to take an HMMT test and not feel bad at getting 1 out of 10 problems correct (or at least to understand that the score is more an indicator of the difficulty of the competition than one's personal abilities).
i think this is a really important point: i know one of my friends, when she took HMMT, actually found that struggling through all the problems and getting a close to 0 score was a good experience because it showed her how much more she had to learn. but she was from a top-10 team and she'd grown up around people who'd qualified for and won olympiads, whereas our hypothetical person from alabama would likely be far more discouraged.
> But contests should be more inclusive. Math education should be a level playing field for everyone. While not everyone can make it to the IMO, the first stage of selection for US IMO team should not feel unnecessarily brutal. A good math education should decrease the gap with the rich and poor, or at least level the playing field.
But nowadays, doing well on prestigious math competitions seems only feasible for those whose parents can afford to send them to high quality training programs or camps that teach math and math competition well, while those whose parents cannot afford such things are left in the dust (much more so than 10 years ago).
So the well-off get more educated, while the poor remain left behind.
yes yes 1000 times yes
I agree. I wrote an additional point on AoPS (I am hurdler).
I totally agree! From experience, I can say that struggling to solve most of the problems on a competition can be demoralizing and an unhelpful experience.
I thought about one Evan quote saying that generally the reason why not everyone takes the USAMO is because scoring zero is demoralizing and totally unhelpful (as I stated above) and that's why the process is in place - to only have the people who will be able to make progress and enjoy the problems fully actually take the test. Why take a test if you're not going to make any progress? That's just a bad idea.
note: this is olyhero
thank you for sharing your experience and perspective!
As someone who also participated in many math competitions when I was younger, it was definitely cool to read about some of these processes and thoughts that went into creating the problems. I wish I enjoyed them as much as you did though, haha. I was one of those kids that wasn't too bad at math, didn't enjoy but didn't hate math competitions either, and got pushed by my parents.
glad you enjoyed it!
I am not even sure ego is the main issue (responding to a comment later down the thread). At least for collegiate contests my guess is that it's lack of experience and not negligence. e.g. HMMT February problem czars are typically writing the February contest for the first time, are only a few years out of high school.
It's easy to say "we should make sure the contest is accessible". It's hard to actually make the judgment calls of "let's use problem X versus problem Y because X will probably be solved by about 80% of students while Y will be solved by about 50%, even though Y is more elegant". The issue is that, without tons of experience working with students, it's nearly impossible to know what those percentages will be. (I still get these decisions wrong all the time myself, look at JMO 2021.) It's doubly true if you're an IMO multi-medalist for which all the problems feel easy anyways. It's triply true if you are in a situation where you didn't have time to personally solve every single proposal (e.g. IMO jury).
Putnam is the only example I can think of where median scores of zero are a source of pride. Every other contest, the usual response upon seeing the statistics of the exam is "oh crap, we messed up". It's part of what makes contest design so difficult, that even assessing the difficulty of a single problem in isolation is perniciously slippery.
(Also, with regard to JMO 2021 -- I don't know the exam but errors are magnified a lot more on such a short exam; I don't think 6 problems is large enough ... whereas if you have 30 problems to work with I'm *certain* it's possible to make a subset of them quite accessible)
> I am not even sure ego is the main issue (responding to a comment later down the thread). At least for collegiate contests my guess is that it's lack of experience and not negligence. e.g. HMMT February problem czars are typically writing the February contest for the first time, are only a few years out of high school.
I'm not sure I agree that it's lack of experience and not negligence; my reasoning would be that HMMT has this problem ... literally every year, right?
Even if you're only writing / organizing the contest for the first time, you have years' worth of data to work with. At that rate I'd be pretty confused if year after year you still end up with the same problem -- way too many zeroes and low scores. I would attribute this more to negligence at this rate, in the sense that if you're a new problem czar and you're not actively looking to try and make the contest easier you are being negligent, right?
I understand how you feel about problems being hard to judge, but this is why people other than the problem czar themselves exist. The head organizer has a huge pool of people to draw on that aren't all MOP/IMO-level -- surely they can find someone who only qualified for AIME in high school, for example, or even just attempted the AMC and didn't necessarily qualify. I would say that if a problem czar isn't actively trying to include people of all different skill levels in the process of setting a test that this is pretty much negligence *due to* inexperience, but at that point we're arguing semantics ... I suppose I was lucky in this sense because I used my 6th-grade brother as a guinea pig multiple times during the process.
I agree we're arguing semantics :) my point was that to people without much experience working with students, their calibration of student's ability is usually far off, whether they realize it or not (and usually they don't).
In particular, if you want a post like this to be useful advice (rather than merely correct advice, which it is), you'd want to give some concrete suggestion of how to improve calibration. Telling people they suck at something (that they do suck at) is a fine first step but begs the question "how to improve?".
In other words, I would say the _how_ to make problems accessible is much more important that _why_ here (along the lines of your reply). I think it's hard to find an HMMT problem czar who disagrees with not zero-ing out half the kids. They just don't know how to get there.
fair enough :P I admit to not giving the most specific advice of all time, but also, how much *specific* advice is there to give? I think “write easy but interesting problems” isn’t a terrible start, and probably gets you more than half the way there …
I suppose I can add another section detailing random things I also did (?!?) thanks for the advice :P
> Of course, there are other contests where many students don’t solve any problems — perhaps the USAMO is a good example — but the point of the USAMO is not to raise interest in math; anyone taking this exam is a top-500 math student in the nation.
It's not a "good" example in the sense that we think it's also a pretty bad experience to solve no problems on a nine-hour exam. But it's tough when you only get three problems each day.
yeah >.> i am familiar with the experience LOL
Is it weird that I feel like the main "problem" in USA based competition is usually the time limit is too low?
I feel like if we allow more time (like even an additional 30 minutes), and probably adding 1-2 more easier problems (which is fair, since we allow more time) for those university contest, it could be a more encouraging experience to the participants.
This is even applicable to AMC, although honestly I'm not really familiar with USA competition scene anymore, but I am pretty sure there was a problem in recent AMC 12 that includes SFFT / telescoping (where I think it's pretty hard to see the pattern) in their first 10 problems (I think SFFT / telescoping of that kind is hard for newer students, since they are not exposed with math competition techniques, newer student tend to play around with patterns and such). While I understand this is to cater people for AIME qualifying purpose (since the skillbar is already higher), but I feel like the difficulty curve could be smaller if we add more time (hence more problems --> better difficulty curve) to accommodate the newer student as well (they could solve more problems as well as they don't feel rushed because of the time limit). An example from my first thought is there could be a 100 minute test - 40 problems.
What do you think about this?
you have some interesting ideas here -- i think the one major qualm i have with *increasing* the time limit is that higher amounts of time are actually a turnoff. imagine if the AMC were 2 hours instead of 1.25 hours. i think less newer students would want to take it then -- longer contests are more intimidating by their nature.
i think a better idea might be in my reply to Xinke in the comments section -- instead of making a cutoff based on percentiles, just make the cutoff based on ability. that way people aren't just left in the dust when their peers who've been studying for ages qualify for AIME.
i think i'd honestly prefer to reduce the time by 15 minutes, say, and probably cut the contest down to 20 problems (or smth similar like this). i think this would probably lead to an increase in number of participants! but if this were to happen they would really, really need to fix the difficulty curve :P
Fair, I'm not from USA (although I was interested in USA competition scene) so I don't know how the students behave there, but in my country, we are used to longer time limit.
i think that longer time limits are good to support more depth of thinking and less "trick-based" approaches to problems, unfortunately i think this would turn more kids off to the contest : ' (
related anecdote: one of my math-adjacent friends told me that she finally gave up on mathcomps after zeroing pumac (which this year was just ridiculously hard for no reason--even i struggled a *lot*). at the time i found it rather surprising since i attach very little weight to my scores on college contests, but i think there may be a real effect here
yes! this is something which has tangible effects on people -- there's no reason for a strong math student (i do know the person in question -- she qualified for AIME and scored quite above average on it) to get a 0 on a contest like PUMaC
so tl;dr write easier but good problems? okay?
idk if this is supposed to be like new ? this is what i strive for when i write problems anyway (which is why hard problems ive written are very scant; most problems ive gotten into contests are easier)
why are you sectioning the blog post with numbers when you can section it with… section titles… that you already have…
hey i wouldn't have written this if half the contests out there *didn't* do this :| i think there's also a lot more to this than just "write easier problems"; surface-level this is the advice for contest writers but i think it's a lot more about not letting your ego get in the way of effective design, which is a principle applicable to lots of things
and in any case there's nothing wrong with rehashing something important that a lot of people don't pay attention to :)
hm i guess my dispute is whether half the contests out there do this or not and i guess i am less familiar with the contest ecosystem here
i told you this elsewhere, but you can check through PUMaC's stats from last year: I skimmed the div B results for algebra and geometry, and in each about 25% of the competitors solved one or less problems. i think this is definitely Not Close to optimal
i mean in this case -- almost AoPS mocks are created for vanity's sake, from what i can tell (oh, i can write a mock? and show off my skills?); HMMT has serious problems; putnam is almost nonsensical in this regard -- i don't know why it's a symbol of pride or smth that so many people get zeroes; ... even some other student-run contests at colleges have the problem that their earlier problems are just not very interesting. I know MMATHS had problems regarding this (and difficulty gradient) in the past so ... /shrug