50 Million Math Question Fans Can't Be Wrong! (OR CAN THEY)

[jonah]

What does this mean? Neither of these things happen currently*, unless you consider the current philosophy and math distributions to be "punishing" those subjects. As people have mentioned before, it's not really possible to write more questions in those subjects while maintaining decent conversion levels.

That's certainly not true of math.

[Charles Martel]

I think the problem with 20/20 is that we're forced to choose between (A) punishing certain categories, such as philosophy and math, and (B) varying the distribution from round to round, which is also undesirable.

What does this mean? Neither of these things happen currently*, unless you consider the current philosophy and math distributions to be "punishing" those subjects. As people have mentioned before, it's not really possible to write more questions in those subjects while maintaining decent conversion levels.

* Unless you consider NAQT, but I don't think NAQT distributes by the set rather than by the round to avoid punishing categories, whatever that means.

Plenty of tournaments shove math into the "minor science" category and then write 3/3 over 13 rounds, which is definitely "punishing" math. Tournaments such as IMSANITY, LIST, and others that included 1/1 math have proven that it's possible to maintain high conversion levels. I think that .5/.5 Philosophy is being unfair to it, but this is certainly arguable.

My second point is that having distributions with numbers not divisible by .5 in them (i.e. .6/.6 Geo) is undesirable, because then the number of questions in that category varies from round to round (whereas .5/.5 Geo will always come up once per round). I don't think the variability of sets should include different distributions in each round.

[Mechanical Beasts]

My second point is that having distributions with numbers not divisible by .5 in them (i.e. .6/.6 Geo) is undesirable, because then the number of questions in that category varies from round to round (whereas .5/.5 Geo will always come up once per round). I don't think the variability of sets should include different distributions in each round.

The reason NAQT distributes by set and not by round is because frequently you do want .6/.6 of something. And, in fact, many people would call your ".6/.6 of X and .9/.9 of Y" something different, like ".5/.5 A and 1/1 B." Take, for example, the top-level NAQT distribution for literature, which formally contains religious literature and mythology but also, of course, sets strict quotas for non-myth and non-religious literature. ACF would put those--along with top-level-code TH:, theology--into RMP. So let's say that about 2/3 of R questions (per ACF) are L:R:; let's say that all myth is L:M:; let's say that the standard ACF distribution has 2/2 RMP per round (except at trash-free nationals, it has 2 or 2.5, usually). Then the difference between NAQT and ACF is just one of accounting, because there's about .44/.44 L:R: per ACF round (and 5.44 L: all told).

Every distribution has fractional subdistributions (poetry! content about the 1300s!); you can find round-to-round asymmetries in any system. NAQT and ACF are two distributions that minimize those asymmetries in different ways.

[SirT]

Plenty of tournaments shove math into the "minor science" category and then write 3/3 over 13 rounds, which is definitely "punishing" math. Tournaments such as IMSANITY, LIST, and others that included 1/1 math have proven that it's possible to maintain high conversion levels. I think that .5/.5 Philosophy is being unfair to it, but this is certainly arguable.

My second point is that having distributions with numbers not divisible by .5 in them (i.e. .6/.6 Geo) is undesirable, because then the number of questions in that category varies from round to round (whereas .5/.5 Geo will always come up once per round). I don't think the variability of sets should include different distributions in each round.

That's really just your opinion. One could also make an argument that tournaments "punish" Earth Science because its only given 25% of the minor science distribution. However, much like with math, that's really not true at all. Your example is also sort of extreme--the correct response to having math constitute less than 25% of the distribution is certainly not to expand the number of questions! Math should make up a majority of the Math/CS distribution in high school and if it gets shafted, that's the set writer's fault, not the distribution's. Also, IMSANITY proved nothing.

As Max alluded to above, anyone arguing for the expansion of Philosophy or Social Science has no clue about their answerability.

[Dominator]

The reason NAQT distributes by set and not by round is because frequently you do want .6/.6 of something.

I think using NAQT as the counterexample here misses the point. NAQT is much more highly structured than, say, housewrites. However, NAQT has a lot of experience taking a micro-managed distribution and making it into a good set. If a housewrite, on the other hand, claims to put .6/.6 of something into a set, it feels like the distro has been proscribed by what was written than prescribed by what a good distro is. So, I think you are countering an argument Adam was not making.

Also, IMSANITY proved nothing.

This point is absolutely right. Having a tournament write tons more math than is currently found in most tournaments while still being both converted and enjoyed is completely irrelevant to this argument. Stop wasting our time, Adam.



As for my two cents, I do not think that the discussion about whether 24/24 will prevent upsets is logical. Upsets are defined as an underdog beating a favorite, and a team can only be a favorite if they are more likely to win given the rules of the game. Changing the distro, and thus the game, redefines the underdog/favorite relationship and renders comparisons difficult at best. Instead, the question should be "Would a 24/24 distribution better serve the needs of quizbowl?". I think Adam's point is that, yes, in some ways it would help certain categories be represented better than the roundoff errors imposed by a 20/20 set, so that should be the conversation. Mathematically speaking, yes, 24/24 does help achieve a finer distribution, but I think that the overall effect will be minimal (like 1 or 2 questions different per set in a category), especially compared to the other effect of making quizbowl tournaments longer. For a premier or national tournament, though, it is an interesting idea.

[Mewto55555]

Well, speaking as someone who absolutely loves math, both in quizbowl and outside it, I don't necessarily think that "look how much math is accessible" and "math is SO COOL" are necessarily good reasons to call for a blanket-wide expansion of math's distribution in quizbowl. Places like IMSA and Ladue have people who really like math, so we write more math into our housewrites; it's our prerogative to do so. Other tournaments lump in math into other science; that's totally cool too. Expanding one area of the distribution necessarily cuts into the frequency of the other areas, there's no way around it. LIST does this by cutting into hard-to-write categories like social science and philosophy; I'm sure IMSAnity makes deeper cuts elsewhere as well. Expanding a game to 24/24 doesn't prevent this from happening, it merely masks the effect. In a 20/20 game with 4/4 of each of the Big Three categories, they combine for 60%. By adding more math, social science, philosophy, or whatever, and expanding to 24/24 causes that total to drop to 50% (this is in fact quite sizable, it'd be like replacing 2/2 in a 20/20 game!)

Also changing to 24/24 is stupid because a lot of high school housewrites seem to be only capable of putting together 12 packets of 20/20 -- if they're going to put in the effort, its much better that they have 14.4 packets of 20/20 than 12 packets of 24/24, even if that 24/24 is necessary for the only possible perfect distribution.


EDIT: Forgot the word "only"

[Dominator]

Well, speaking as someone who absolutely loves math, both in quizbowl and outside it, I don't necessarily think that "look how much math is accessible" and "math is SO COOL" are necessarily good reasons to call for a blanket-wide expansion of math's distribution in quizbowl.

I agree. Who was making that argument?

When you play a high school tournament with more anthropology than math, I consider that a problem. I also have never suggested that tournaments mimic IMSANITY by making 1.5/1.5 math. There is a world of middle ground there, people.

Also changing to 24/24 is stupid because a lot of high school housewrites seem to be capable of putting together 12 packets of 20/20 -- if they're going to put in the effort, its much better that they have 14.4 packets of 20/20 than 12 packets of 24/24, even if that 24/24 is necessary for the only possible perfect distribution.

This is true, but it is more of a point that the way housewrites are written needs reform than that the distribution does not need reformed. (I'll reiterate here that I am not advocating one way or the other.)

[Mewto55555]

Well, speaking as someone who absolutely loves math, both in quizbowl and outside it, I don't necessarily think that "look how much math is accessible" and "math is SO COOL" are necessarily good reasons to call for a blanket-wide expansion of math's distribution in quizbowl.

I agree. Who was making that argument?

When you play a high school tournament with more anthropology than math, I consider that a problem. I also have never suggested that tournaments mimic IMSANITY by making 1.5/1.5 math. There is a world of middle ground there, people.

I mean, the only pro-math arguments so far in this thread have been that there are a number of precedents which show that X/X math can indeed be accessibly written for some relatively large values of X, and things along the lines of "I feel math is getting punished and no set can possibly be reasonably reasonable without having at least 0.5/0.5 math per round." Any particular distribution is relatively arbitrary; there's no real reason I can't also just say "when you play a high school tournament with more literature than math, I consider that a problem," except for the fact that it'd be a rather silly thing to say, given the current relative importance of the two in terms of quizbowl. The best middle ground is most likely that we keep 20/20 for no other reason than that it works well, and individual editors can decide what distribution works best for their set.

[Scaled Flowerpiercer]

I mean, the only pro-math arguments so far in this thread have been that there are a number of precedents which show that X/X math can indeed be accessibly written for some relatively large values of X, and things along the lines of "I feel math is getting punished and no set can possibly be reasonably reasonable without having at least 0.5/0.5 math per round." Any particular distribution is relatively arbitrary; there's no real reason I can't also just say "when you play a high school tournament with more literature than math, I consider that a problem," except for the fact that it'd be a rather silly thing to say, given the current relative importance of the two in terms of quizbowl. The best middle ground is most likely that we keep 20/20 for no other reason than that it works well, and individual editors can decide what distribution works best for their set.

As an ardent fan of math as well, I would love to see it come up far more in quizbowl, and I will contribute my math related argument as there don't seem to be too many good ones, in face most of the arguments here have just been of the form "I want 24/24 because it means more math," not "quizbowl should have more math for [reason other than that I like it]" When Comp Math tossups were the norm, Comp math had at least a 1/1 distribution, if not 1.5/1.5 in most sets (if I am not in error), and I don't think that a shift from Comp math to good math should mean that math, as a whole, gets hurt in terms of its importance - not to mention that non Comp math is more accessible/convertible than Comp math, and thus it should constitute a larger portion of a distribution, not less.

Though I love math - to the point that I think when my team likely has to attend nationals over HSNCT I will miss noncomputational math more than I will miss pyramidality - I think that it is improper to use the 24/24 argument as a proxy for asking for more math, I think that math distributions can be reasonably and fairly increased within the constraints of 20/20, and all of the various potential difficulties in switching to 24/24 are not worth it.

[Dominator]

Somehow people keep misconstruing what Adam said as "Let's add 4/4 so I can fit more math in" when he said "Let's add 4/4 so that topics like math AND PHILOSOPHY get a distribution that better reflects their importance". As Adam's coach, I can tell you that there is absolutely no self-interest in him advocating for more philosophy. To make progress, this thread should stop trying to convince itself that Adam is trying to change quizbowl so that he'll be better at it.

When Adam talked about subjects being punished, he was specifically talking about the situation in which the number of questions from a given subject varies because the amount of it that should appear in any round is not a multiple of 5%. If we can agree that something should appear, say, 8% of the time, a 24/24 distribution would treat it more fairly, round per round, than a 20/20 one would.

[Sulawesi Myzomela]

Also changing to 24/24 is stupid because a lot of high school housewrites seem to be capable of putting together 12 packets of 20/20 -- if they're going to put in the effort, its much better that they have 14.4 packets of 20/20 than 12 packets of 24/24, even if that 24/24 is necessary for the only possible perfect distribution.

I think one popular idea going forward is that most high school housewrites will involve a few schools working together to create a set instead of one school doing it all. LIST is great from what I hear, but the same can't be said for a lot of tournaments written by one school. Why not have 15 packets of 24/24, with roughly a third of each tournament coming from each of 3 schools collaborating on a set? That's the equivalent of each school contributing six 20/20 packets, roughly half of what they would if they wrote an event by themselves.

The point being, an extra 4/4 a round though allows schools to get a little more writing experience when they are collaborating on a tournament. If schools still want to write a tournament by themselves, than 20/20 probably is still the best amount for them.

[SirT]

Also, IMSANITY proved nothing.

This point is absolutely right. Having a tournament write tons more math than is currently found in most tournaments while still being both converted and enjoyed is completely irrelevant to this argument. Stop wasting our time, Adam.

Sure, a lot of math tossups in IMSANITY were convertable after the question was finished--really, who can't get a question that basically ends with "what is two times eleven plus one"? That doesn't mean the tossups were accessible or good and thus proved anything though.

Somehow people keep misconstruing what Adam said as "Let's add 4/4 so I can fit more math in" when he said "Let's add 4/4 so that topics like math AND PHILOSOPHY get a distribution that better reflects their importance". As Adam's coach, I can tell you that there is absolutely no self-interest in him advocating for more philosophy. To make progress, this thread should stop trying to convince itself that Adam is trying to change quizbowl so that he'll be better at it.

I fail to see where this charge is leveled against Adam. Once again, as numerous people have noted throughout this thread, increasing Philosophy in high school quizbowl is a very bad idea and will just result in a lots of dead tossups. Any argument for an increase in the number of questions in a round based on "we need more Philosophy (or Social Science, for that matter)" is a bad argument.

[Grams's Go-Go Boots]

Also, IMSANITY proved nothing.

This point is absolutely right. Having a tournament write tons more math than is currently found in most tournaments while still being both converted and enjoyed is completely irrelevant to this argument. Stop wasting our time, Adam.

I'm calling this into doubt due to three distinct issues:

1) I don't believe there was actual conversion info on both tossups & bonuses.

2) We don't have information on buzz points, so conversion info on tossups is limited.

3) IMSANITY 1 & 2 were only played in Illinois, with fields that are in the top quartile (at a minimum) of field strength in the country.

[Kenneth Widmerpool]

This point is absolutely right. Having a tournament write tons more math than is currently found in most tournaments while still being both converted and enjoyed is completely irrelevant to this argument. Stop wasting our time, Adam.

I could write a tournament with tons more video games and history than is currently found in most tournaments while still being both converted and enjoyed. What would I be proving by doing so?

[Mewto55555]

Somehow people keep misconstruing what Adam said as "Let's add 4/4 so I can fit more math in" when he said "Let's add 4/4 so that topics like math AND PHILOSOPHY get a distribution that better reflects their importance".

Even if that is the case, why does it have to be through some expansion to 24/24? If hypothetical subject PHILOMATH absolutely needs to come up around 8% of the time for whatever reason, then we can do this incredibly unreasonable thing where it comes up 2/1 one round and 1/2 the next, for a total of 7.5%. I'm hardly convinced that this takes up a lot of unreasonable work and silly question writers will manage to screw it up or that this optimal distribution is so fine-tuned that 7.5% is beyond a reasonable margin of error (if this is a HUGE PROBLEM we can still get close to the value of 8.3333% achieved by the brilliant but impractical 24/24 solution by cycling through 2/1,1/2, and 2/2 every three rounds, to achieve a value of, you guessed it, 8.3333%).

Also, it still remains unaddressed that distribution is a zero-sum game; any increase in PHILOMATH necessarily comes at the expense of the influence of the rest of the categories -- mathematically we should realize we can't just wish this away by making packets harder for people to write, as it will happen regardless of whether packets are 20/20 or 24/24. If we're going to try to increase PHILOMATH, we should discuss increasing PHILOMATH based on the merits of PHILOMATH.

[Charles Martel]

I'm calling this into doubt due to three distinct issues:

1) I don't believe there was actual conversion info on both tossups & bonuses.

2) We don't have information on buzz points, so conversion info on tossups is limited.

3) IMSANITY 1 & 2 were only played in Illinois, with fields that are in the top quartile (at a minimum) of field strength in the country.

First, I'll make a theoretical argument that math should be converted better. High schoolers don't necessarily learn about art history or music history anywhere in their lives. They only need to learn tiny parts of the literature canon. However, high schoolers take math class (nearly) every year in school, and most answer lines at least come up in those classes.

You're right on the first two points. In the room I read, tons of tossups in literature, fine arts, religion, and philosophy went dead. However, I would bet that math was the most converted category aside from trash. There is no hard data on this, but I think that most moderators will testify that the math had high conversion.

On the third point, the tournaments were run in Southern Illinois, with fields fairly representative of national field strength. Not sure about this though. Maybe someone else could try running it somewhere else so we could find out?

Sure, a lot of math tossups in IMSANITY were convertable after the question was finished--really, who can't get a question that basically ends with "what is two times eleven plus one"? That doesn't mean the tossups were accessible or good and thus proved anything though.

Actually, lots of converted tossups does mean the tossups were accessible. The question you are singling out would have definitely gone to the last line in most rooms. However, I believe that's an exception, and most tossups have many buzzable clues in the middle. On the topic of "good": Dr. Noah Prince (Ph. D. in math and math teacher) would call IMSANITY 2 Math good. Jonah Greenthal (majored in math) calls them "okay" (but this is Jonah). The entire overlap that I know of last year's Chicago ARML team and people who have seen IMSANITY 2 (Webster Guan, Anton Karpovich, Andrew Wang, me) would call IMSANITY 2 Math good. Find me someone knowledgeable about math who would say that IMSANITY 2 Math was bad.

Personally, I thought IMSANITY 2 and LIST were a fantastic change from the usual math clue pattern of unbuzzable, unbuzzable, something that Nolan Winkler reflex buzzes on. Although both tournaments used early clues that most people wouldn't know, high schoolers who have spent lots of time studying math outside of school would buzz on many of these early clues.

I could write a tournament with tons more video games and history than is currently found in most tournaments while still being both converted and enjoyed. What would I be proving by doing so?

You would be proving that it's possible to have more history and video games in quizbowl. However, no one is asserting that either is being shorted in quizbowl. Math, on the other hand, has been largely marginalized after the demise of computational math. High Schoolers spend as much time, if not more, in math as science, history, and English class. Most high schoolers spend a single year studying American literature, which takes up 1/1 in quizbowl, so why should math not deserve an equal distribution? Most high schoolers spend a single year learning biology so why shouldn't math deserve an equal 1/1? The entire work of mathematics is large enough to merit at least 1/1, and mathematics is at least as important as either of the prior two.

I will keep arguing for 1/1 math in quizbowl, but I understand adopting .5/.5 as a compromise until the high school math canon expands. What is unacceptable is how playing HSAPQ 22 earlier this year, more anthropology occurred than math.

EDIT: How do quote?
EDIT2: Fixing which HSAPQ set I played

[Kenneth Widmerpool]

I could write a tournament with tons more video games and history than is currently found in most tournaments while still being both converted and enjoyed. What would I be proving by doing so?

You would be proving that it's possible to have more history and video games in quizbowl. However, no one is asserting that either is being shorted in quizbowl. Math, on the other hand, has been largely marginalized after the demise of computational math. High Schoolers spend as much time, if not more, in math as science, history, and English class. Most high schoolers spend a single year studying American literature, which takes up 1/1 in quizbowl, so why should math not deserve an equal distribution? Most high schoolers spend a single year learning biology so why shouldn't math deserve an equal 1/1? The entire work of mathematics is large enough to merit at least 1/1, and mathematics is at least as important as either of the prior two.

I will keep arguing for 1/1 math in quizbowl, but I understand adopting .5/.5 as a compromise until the high school math canon expands. What is unacceptable is how playing HSAPQ 22 earlier this year, more anthropology occurred than math.

EDIT: How do quote?
EDIT2: Fixing which HSAPQ set I played

Nobody but the people in this thread have asserted that math has been marginalized after the demise of comp math and no evidence has been produced to back that up. Right now it seems like an is-ought problem to me -- maybe you can write 3/3 possible math per round in a hs set, but I don't see why you ought to.

[Charles Martel]

HSAPQ 22 contained 3/3 math total, 0/2 of which appeared in the rounds that were played. The majority of tournaments written have less than .5/.5 math per round, although I can't post exact numbers because I don't know them. I said a post earlier that I consider 1/1 to be the ideal, not 3/3, so stop saying that I'm arguing for 3/3.

[Matt Weiner]

HSAPQ 22 contained 3/3 math total, 0/2 of which appeared in the rounds that were played. The majority of tournaments written have less than .5/.5 math per round, although I can't post exact numbers because I don't know them. I said a post earlier that I consider 1/1 to be the ideal, not 3/3, so stop saying that I'm arguing for 3/3.

HSAPQ has been discussing this issue internally for a little while, and I have an announcement in the works that I think many people will find agreeable.

[jonah]

Nobody but the people in this thread have asserted that math has been marginalized after the demise of comp math and no evidence has been produced to back that up. Right now it seems like an is-ought problem to me -- maybe you can write 3/3 possible math per round in a hs set, but I don't see why you ought to.

If I understand it correctly, Adam's point—which I agree with, mostly—is that math has the following properties:

• In most distributions of current quality high school sets sets, there are few math questions.
• In high school sets, well-written math questions will see some of the best conversion numbers of any category because of the amount of math that most high school students study (a lot) and the way in which it is taught (pretty similar across the country, whereas for example, people will likely read wildly different sets of books in their literature classes).
• Several high school tournaments recently have given empirical evidence, albeit not as much as some people would like, for the above statement, while remedying the first issue (by having more math questions than is usual).
• It is generally a goal of set writers and editors to have high conversion numbers, given other reasonable constraints that aren't really at issue here.
• Therefore, increasing the amount of math questions in high school sets would help accomplish writers' and editors' goals while having a nondetrimental, and probably beneficial, effect on the players of said sets.

[Smuttynose Island]

So although it's a little bit of a sidetrack I think that this is a decent opportunity for me to point out a few of what I consider to be "fundamental" errors of thinking when it comes to how a fair number of people determine whether or not a question is good.

Sure, a lot of math tossups in IMSANITY were convertable after the question was finished--really, who can't get a question that basically ends with "what is two times eleven plus one"? That doesn't mean the tossups were accessible or good and thus proved anything though.

Actually, lots of converted tossups does mean the tossups were accessible.

Actually it doesn't. Just because TUs are converted doesn't mean that they are "accessible." As Cody pointed out earlier, accessibility relies just as much on what clues you use throughout the TU as it does the difficulty of your answerline. I could write a TU on the number 2 and use a bunch of random and difficult clues that no one in the country could buzz off of and then end the TU with "For 10 points, give this number that is equal to one plus one." Just because everyone playing that question would convert it doesn't mean that the TU was "accessible."

On the topic of "good": Dr. Noah Prince (Ph. D. in math and math teacher) would call IMSANITY 2 Math good. Jonah Greenthal (majored in math) calls them "okay" (but this is Jonah). The entire overlap that I know of last year's Chicago ARML team and people who have seen IMSANITY 2 (Webster Guan, Anton Karpovich, Andrew Wang, me) would call IMSANITY 2 Math good. Find me someone knowledgeable about math who would say that IMSANITY 2 Math was bad.

I'd also like to point out that just because someone knows a lot of math, be it because they have a Ph. D. in the subject, majored in it, does it as an activity, or simply enjoys its beauty, does not mean that they are capable of determining whether a math TU is good or not. When it comes to determining if a TU is "good," being able to discern if the TU was written well, contains buzzable and unique clues, which are structured correctly is much more important than being a so called "expert" in a field. For example, I don't know much about Things Fall Apart, but I'm still able to look at certain clues and with a little bit of research determine if they are in a fairly correct order and are written in a buzzable manner. To be clear, I'm not trying to say that Dr. Prince or Jonah don't know what they are doing, just that, should they know what they are doing, it is not for the reasons that you listed, although those can help some.

[in on these shenanigans]

On the topic of "good": Dr. Noah Prince (Ph. D. in math and math teacher) would call IMSANITY 2 Math good. Jonah Greenthal (majored in math) calls them "okay" (but this is Jonah). The entire overlap that I know of last year's Chicago ARML team and people who have seen IMSANITY 2 (Webster Guan, Anton Karpovich, Andrew Wang, me) would call IMSANITY 2 Math good. Find me someone knowledgeable about math who would say that IMSANITY 2 Math was bad.

I'd also like to point out that just because someone knows a lot of math, be it because they have a Ph. D. in the subject, majored in it, does it as an activity, or simply enjoys its beauty, does not mean that they are capable of determining whether a math TU is good or not. When it comes to determining if a TU is "good," being able to discern if the TU was written well, contains buzzable and unique clues, which are structured correctly is much more important than being a so called "expert" in a field. For example, I don't know much about Things Fall Apart, but I'm still able to look at certain clues and with a little bit of research determine if they are in a fairly correct order and are written in a buzzable manner. To be clear, I'm not trying to say that Dr. Prince or Jonah don't know what they are doing, just that, should they know what they are doing, it is not for the reasons that you listed, although those can help some.

If I've got a decision to make between someone who understands even just the basic axioms of quizbowl (like what a "clue" is and why they need to go in hard-medium-easy order in a tossup) and was a math enthusiast in college - anywhere from math major to Ph. D. - OR someone who doesn't do dedicated work in math but has read many quizbowl packets, there's no doubt in my mind that the former's going to write a better math question than the latter. The reason? The math enthusiast stands a much better chance of A: understanding the material well enough to write an accurate question, B: having deep enough knowledge to write non-misleading, unique, interesting leadins, and (most importantly!) C: knowing what people in the tournament's audience will know. There have been far too many math tossups in the last two years that simply rattle off eponymous theorems (that's what Adam's referring to with the Nolan Winkler reflex buzz, I'm sure) and/or tossup horribly conceived ideas like 'answer: _group_s" at the high school level. These things didn't happen in IMSAnity, they don't happen when Jonah or I edit a set, and they do happen frustratingly often when we play high school housewrites like DAFT.

Am I saying you need a math degree to write good questions? No - because then we'd all be screwed and no tournament would ever get written. But, empirically, math degree work makes you better at recognizing problems with math questions and you just don't get that from hearing a thousand questions that namedrop Ceva's theorem.

[ether a go-go]

Sorry to take this further afield.

As somebody who writes a lot of questions and is married to a doctor who doesn't know much about quizbowl, I consider myself qualified to tell Brad that he is completely wrong. My wife will sometimes tell me that I should write a question on some particular thing she suggests, and that thing almost always turns out to be something obscure or unimportant--she doesn't quite believe me that something like diabetes or calcium is a good answer. When I tell her what I'm writing about, she makes clue suggestions that are obscure or not uniquely identifying or take fifty words to explain. She is good at what she is good at, which is many things, but writing questions or evaluating questions isn't one of those things, because she doesn't really understand quizbowl all that well. I occasionally use her as a sounding board--I'll read the first line of a tossup to her to see if she knows the answer, which is a way for me to know whether I made sense and used a uniquely identifying clue--but that's the extent of her contribution. If she wanted to get good at writing questions, she would need to write a few questions, have them critiqued, write a few more questions, have them critiqued and perhaps playtested in front of her, read some examples of good questions, etc.

To get back on the last tangent this thread was on, I too would like to see math regularly become 1/1 at least, and I agree with many of the reasons above--people new to the game have a better chance of knowing some math than they do of knowing social science, which at the high school level becomes a test of who has studied the most for quizbowl, which as far as I can tell does not lead to students doing much more than memorizing titles and a few buzzwords. One problem with suddenly upping the math distribution, however, is that some writers are uncomfortable with it or bad at it, due in part to the fact that they haven't heard lots of regular high school level math questions. I think this is a change that will happen and perhaps is happening, though it may be a slow uneven process. Since our activity is largely decentralized, and there isn't a consensus on this point, the fact that change is uneven shouldn't surprise anybody.

[SirT]

Sure, a lot of math tossups in IMSANITY were convertable after the question was finished--really, who can't get a question that basically ends with "what is two times eleven plus one"? That doesn't mean the tossups were accessible or good and thus proved anything though.

Actually, lots of converted tossups does mean the tossups were accessible. The question you are singling out would have definitely gone to the last line in most rooms. However, I believe that's an exception, and most tossups have many buzzable clues in the middle. On the topic of "good": Dr. Noah Prince (Ph. D. in math and math teacher) would call IMSANITY 2 Math good. Jonah Greenthal (majored in math) calls them "okay" (but this is Jonah). The entire overlap that I know of last year's Chicago ARML team and people who have seen IMSANITY 2 (Webster Guan, Anton Karpovich, Andrew Wang, me) would call IMSANITY 2 Math good. Find me someone knowledgeable about math who would say that IMSANITY 2 Math was bad.

I am most certainly not cherry-picking examples here--that just happened to be the first thing that came to mind because of just how memorably awful it was. The entire IMSANITY set (note that I am talking about IMSANITY 1 here) is full of bad questions of varying forms, in math and elsewhere, and plenty don't have buzzable clues in the middle. Just browsing through the first two rounds, cubic and gcd are impossible to power unless you've done ARML or something, algebra bizarrely drops linear type before describing and naming the abstract type (and what the hell was someone thinking having sigma algebras even as a clue in a regular high school set/great giveaway you've got there!) and I won't even get into the tossups on TSP and while loop that were grouped under Math as I recall.

Also, considering that the above people (excepting Jonah Greenthal) were responsible for the IMSANITY math last year, why in the world would I trust their opinion this year?

You would be proving that it's possible to have more history and video games in quizbowl. However, no one is asserting that either is being shorted in quizbowl. Math, on the other hand, has been largely marginalized after the demise of computational math. High Schoolers spend as much time, if not more, in math as science, history, and English class. Most high schoolers spend a single year studying American literature, which takes up 1/1 in quizbowl, so why should math not deserve an equal distribution? Most high schoolers spend a single year learning biology so why shouldn't math deserve an equal 1/1? The entire work of mathematics is large enough to merit at least 1/1, and mathematics is at least as important as either of the prior two.

Again, I can make the exact same argument for Earth Science--why isn't Earth Science, a class you spend as much time in as Biology, given the same importance as the other "big three" sciences? You can make these sort of comparisons all you want, but they're all pointless when you get down to it.

If I've got a decision to make between someone who understands even just the basic axioms of quizbowl (like what a "clue" is and why they need to go in hard-medium-easy order in a tossup) and was a math enthusiast in college - anywhere from math major to Ph. D. - OR someone who doesn't do dedicated work in math but has read many quizbowl packets, there's no doubt in my mind that the former's going to write a better math question than the latter. The reason? The math enthusiast stands a much better chance of A: understanding the material well enough to write an accurate question, B: having deep enough knowledge to write non-misleading, unique, interesting leadins, and (most importantly!) C: knowing what people in the tournament's audience will know. There have been far too many math tossups in the last two years that simply rattle off eponymous theorems (that's what Adam's referring to with the Nolan Winkler reflex buzz, I'm sure) and/or tossup horribly conceived ideas like 'answer: _group_s" at the high school level. These things didn't happen in IMSAnity, they don't happen when Jonah or I edit a set, and they do happen frustratingly often when we play high school housewrites like DAFT.

Am I saying you need a math degree to write good questions? No - because then we'd all be screwed and no tournament would ever get written. But, empirically, math degree work makes you better at recognizing problems with math questions and you just don't get that from hearing a thousand questions that namedrop Ceva's theorem.

As IMSANITY 1 amply proves, this is simply not true (despite your bizarre assertion to the contrary about the "goodness" of the IMSANITY set). People with expertise in their field knowing the "basic axioms of quizbowl" guarantees diddly squat about their questions compared to someone else. Also, your dichotomy is falsely constructed and stupid.

[cvdwightw]

You would be proving that it's possible to have more history and video games in quizbowl. However, no one is asserting that either is being shorted in quizbowl. Math, on the other hand, has been largely marginalized after the demise of computational math. High Schoolers spend as much time, if not more, in math as science, history, and English class. Most high schoolers spend a single year studying American literature, which takes up 1/1 in quizbowl, so why should math not deserve an equal distribution? Most high schoolers spend a single year learning biology so why shouldn't math deserve an equal 1/1? The entire work of mathematics is large enough to merit at least 1/1, and mathematics is at least as important as either of the prior two.

Again, I can make the exact same argument for Earth Science--why isn't Earth Science, a class you spend as much time in as Biology, given the same importance as the other "big three" sciences? You can make these sort of comparisons all you want, but they're all pointless when you get down to it.

I took two years of biology in high school and I don't think I took anything approximating "Earth Science" after sixth grade. The argument that you want to make is that a subject's importance in quizbowl cannot and should not be measured solely by a subject's importance in the curriculum.

Anyway, having waded into this mess, I just want to say that the conclusion "if 20/20 is not enough, we should play 24/24" has no basis in either logic or historical precedent. To the latter point, TWAIN at UCLA played 21/21 of IS packets for many years; Caltech's Technophobia played packets of 22/22 until the 2005 mess I think. Maybe this was just a California thing, but it doesn't logically follow that you need a "nice round number" of questions to have an enjoyable tournament in which generally teams that know more win more.

[Smuttynose Island]

If I've got a decision to make between someone who understands even just the basic axioms of quizbowl (like what a "clue" is and why they need to go in hard-medium-easy order in a tossup) and was a math enthusiast in college - anywhere from math major to Ph. D. - OR someone who doesn't do dedicated work in math but has read many quizbowl packets, there's no doubt in my mind that the former's going to write a better math question than the latter. The reason? The math enthusiast stands a much better chance of A: understanding the material well enough to write an accurate question, B: having deep enough knowledge to write non-misleading, unique, interesting leadins, and (most importantly!) C: knowing what people in the tournament's audience will know. There have been far too many math tossups in the last two years that simply rattle off eponymous theorems (that's what Adam's referring to with the Nolan Winkler reflex buzz, I'm sure) and/or tossup horribly conceived ideas like 'answer: _group_s" at the high school level. These things didn't happen in IMSAnity, they don't happen when Jonah or I edit a set, and they do happen frustratingly often when we play high school housewrites like DAFT.

I think that your issue here is that you are conflating a person who reads a lot of packets, or an otherwise experienced QB player, with someone who is a good question writer or editor. While a good editor or writer is almost always an experienced quizbowl player, the vast majority of experienced quizbowl players are not good editors or writers. If I need someone to write math questions for my set, especially at the HS level where being especially knowledgeable about a given area is not terribly important, I'd take a good editor or writer with an average understanding of math over the type of person that you described first in your post.

[jonah]

Again, I can make the exact same argument for Earth Science--why isn't Earth Science, a class you spend as much time in as Biology, given the same importance as the other "big three" sciences? You can make these sort of comparisons all you want, but they're all pointless when you get down to it.

I took two years of biology in high school and I don't think I took anything approximating "Earth Science" after sixth grade. The argument that you want to make is that a subject's importance in quizbowl cannot and should not be measured solely by a subject's importance in the curriculum.

Agreed. Earth science is not, in fact, "a class you spend as much time in as biology". Some people might, but I never—not in sixth grade, not ever—took any class along the lines of earth science, and my high school didn't even offer one. (It offered a close-ish class that was not well thought of, called Environmental Geoscience, that spent roughly half its time on earth science and was taken by approximately no high-level students.) On the other hand, I don't have data but I'm pretty sure most high school students take at least two years of math, and many (especially the type of student we expect to be playing quizbowl) take three or four. Even if we suppose that Dwight's and my high school experiences were very anomalous and most high school students take a year of earth science, that's still a ratio of at least twice as much math as earth science.

I am not saying that the distribution should be developed based on high school courseloads. That would be a bad idea for many reasons, and wouldn't be possible except at a local scale even if it were a good idea. But I do think that in some cases—namely, the ones concerning categories in which it is possible to write significant numbers of good questions—, it makes sense to let trends that are universal or nearly universal among the thousands of high school curricula in use across the country have some influence on the distribution we choose.

[SirT]

Apparently I am overgeneralizing my experience with the Virginia curriculum. The point still stands that it's a pointless and stupid argument, though--Dwight pretty much nails what I wanted to say.

[Charles Martel]

If I need someone to write math questions for my set, especially at the HS level where being especially knowledgeable about a given area is not terribly important, I'd take a good editor or writer with an average understanding of math over the type of person that you described first in your post.

Thinking like this is why most math questions in quizbowl bear no resemblance at all to what math is really like, fail to reward any sort of real knowledge in mathematics, and are often incomprehensible and not uniquely identifying.

[SirT]

If I need someone to write math questions for my set, especially at the HS level where being especially knowledgeable about a given area is not terribly important, I'd take a good editor or writer with an average understanding of math over the type of person that you described first in your post.

Thinking like this is why most math questions in quizbowl bear no resemblance at all to what math is really like, fail to reward any sort of real knowledge in mathematics, and are often incomprehensible and not uniquely identifying.

This is manifestly untrue, would you care to provide some examples?

[Smuttynose Island]

If I need someone to write math questions for my set, especially at the HS level where being especially knowledgeable about a given area is not terribly important, I'd take a good editor or writer with an average understanding of math over the type of person that you described first in your post.

Thinking like this is why most math questions in quizbowl bear no resemblance at all to what math is really like, fail to reward any sort of real knowledge in mathematics, and are often incomprehensible and not uniquely identifying.

Not really. Bad math questions have been written because most of the time bad editors or writers are writing said questions, the same can be said about any bad questions.

[Charles Martel]

Second math tossup I found in the last HSAPQ ACF-style regular-season set on their site:

12. This theorem is generalized by de Gua's Theorem. The traditional proof of this statement made
use of the "windmill." When using only integers, it is the highest possible case allowed by Fermat's
Last Theorem. Many proofs of it are based on the dissection of shapes. This formula is also used to
determine the norm of a vector in Cartesian space. It is the general case of the law of (*) cosines. For
10 points, name this theorem used to determine the length of the hypotenuse of a right triangle, written a
squared plus b squared equals c squared.
ANSWER: Pythagorean theorem

My response when I looked up the lead-in clue --- "That has a name?"
Prince's response when he looked it up --- "That has a name?"
The response of any mathematician looking it up --- "That has a name?"
de Gua's theorem is only a thing on mathworld and wikipedia. Pythagoras knew about de Gua's theorem, but didn't bother to name it. It literally consists of applying the Pythagorean theorem twice, and any mathematician would call it "Using the Pythagorean theorem twice."( EDIT: This is wrong, de Gau's theorem is something different than what Dr. Prince, other people, and me thought it was at first glance.)
Mathworld is actually a horrible source to find out what is notable in math. It's about as accurate as wikipedia, except it has bizzarely little information on some notable topics and contains huge amounts of information on some unimportant topics.

"Traditional proof" is an ambiguous statement that could apply to many of the 780 proofs of the Pythagorean theorem. If you don't want to mention Euclid or the Elements, it should at least be "Oldest known proof."

Consider the clue about Fermat's Last Theorem by itself. The correct answer to that clue would be n=2. 2 is different from the Pythagorean theorem.

"Many proofs of it are based on the dissection of shapes." *BUZZ* Most theorems in geometry?

The Pythagorean theorem is a specific case of the law of cosines, not a general case as this question incorrectly stated it. That clue is incorrect and unbuzzable as written.

Even the giveaway isn't exactly accurate (It relates the hypotenuse and legs), but quizbowl math must sometimes sacrifice clarity for conciseness, and this is one of those acceptable instances.

In conclusion, this tossup sucks. Less experienced high school writers often produce even more math tossups of this quality in their sets. Either HSAPQ has bad writers and editors, or good writers and editors with average knowledge of math (Daniel's model math tossup writer) can produce atrocious math tossups.

[Cheynem]

I probably could find less than desireable questions in a number of categories. If you found this question poor, give some feedback to the editors who were working on it (for the record, I don't know who edits math in HSAPQ). I do not own a literature degree, but have edited a number of literature tossups (pretty good ones). I understood the points you were making about this tossup's problems about math, so I would bet even a layman math editor could too.

Also: This apparent difficulty in writing math questions doesn't make me want to include more math in a distribution.

[Smuttynose Island]

Second math tossup I found in the last HSAPQ ACF-style regular-season set on their site:

12. This theorem is generalized by de Gua's Theorem. The traditional proof of this statement made
use of the "windmill." When using only integers, it is the highest possible case allowed by Fermat's
Last Theorem. Many proofs of it are based on the dissection of shapes. This formula is also used to
determine the norm of a vector in Cartesian space. It is the general case of the law of (*) cosines. For
10 points, name this theorem used to determine the length of the hypotenuse of a right triangle, written a
squared plus b squared equals c squared.
ANSWER: Pythagorean theorem

My response when I looked up the lead-in clue --- "That has a name?"
Prince's response when he looked it up --- "That has a name?"
The response of any mathematician looking it up --- "That has a name?"
de Gua's theorem is only a thing on mathworld and wikipedia. Pythagoras knew about de Gua's theorem, but didn't bother to name it. It literally consists of applying the Pythagorean theorem twice, and any mathematician would call it "Using the Pythagorean theorem twice." Mathworld is actually a horrible source to find out what is notable in math. It's about as accurate as wikipedia, except it has bizzarely little information on some notable topics and contains huge amounts of information on some unimportant topics.

"Traditional proof" is an ambiguous statement that could apply to many of the 780 proofs of the Pythagorean theorem. If you don't want to mention Euclid or the Elements, it should at least be "Oldest known proof."

Consider the clue about Fermat's Last Theorem by itself. The correct answer to that clue would be n=2. 2 is different from the Pythagorean theorem.

"Many proofs of it are based on the dissection of shapes." *BUZZ* Most theorems in geometry?

The Pythagorean theorem is a specific case of the law of cosines, not a general case as this question incorrectly stated it. That clue is incorrect and unbuzzable as written.

Even the giveaway isn't exactly accurate (It relates the hypotenuse and legs), but quizbowl math must sometimes sacrifice clarity for conciseness, and this is one of those acceptable instances.

In conclusion, this tossup sucks. Less experienced high school writers often produce even more math tossups of this quality in their sets. Either HSAPQ has bad writers and editors, or good writers and editors with average knowledge of math (Daniel's model math tossup writer) can produce atrocious math tossups.

To begin with, this was not HSAPQ's last ACF set. HSAPQ continues to produce ACF sets to this day. Secondly, never in this entire thread have I explicitly stated that even good editors or writers always produce great questions, just that, on average, they will produce better questions in any given subject area. Until you can produce a wealth of evidence to undermine that claim, in other words one TU, just as it never does, isn't going to cut it, I am going to chose that proven editor or writer over some math lover. Also it is possible that a not so great writer produced that question and that it then got through the editing cracks, HSAPQ isn't perfect.

[Vernon Lee Bad Marriage, Jr.]

Second math tossup I found in the last HSAPQ ACF-style regular-season set on their site:

12. This theorem is generalized by de Gua's Theorem. The traditional proof of this statement made
use of the "windmill." When using only integers, it is the highest possible case allowed by Fermat's
Last Theorem. Many proofs of it are based on the dissection of shapes. This formula is also used to
determine the norm of a vector in Cartesian space. It is the general case of the law of (*) cosines. For
10 points, name this theorem used to determine the length of the hypotenuse of a right triangle, written a
squared plus b squared equals c squared.
ANSWER: Pythagorean theorem

My response when I looked up the lead-in clue --- "That has a name?"
Prince's response when he looked it up --- "That has a name?"
The response of any mathematician looking it up --- "That has a name?"
de Gua's theorem is only a thing on mathworld and wikipedia. Pythagoras knew about de Gua's theorem, but didn't bother to name it. It literally consists of applying the Pythagorean theorem twice, and any mathematician would call it "Using the Pythagorean theorem twice." Mathworld is actually a horrible source to find out what is notable in math. It's about as accurate as wikipedia, except it has bizzarely little information on some notable topics and contains huge amounts of information on some unimportant topics.

"Traditional proof" is an ambiguous statement that could apply to many of the 780 proofs of the Pythagorean theorem. If you don't want to mention Euclid or the Elements, it should at least be "Oldest known proof."

Consider the clue about Fermat's Last Theorem by itself. The correct answer to that clue would be n=2. 2 is different from the Pythagorean theorem.

"Many proofs of it are based on the dissection of shapes." *BUZZ* Most theorems in geometry?

The Pythagorean theorem is a specific case of the law of cosines, not a general case as this question incorrectly stated it. That clue is incorrect and unbuzzable as written.

Even the giveaway isn't exactly accurate (It relates the hypotenuse and legs), but quizbowl math must sometimes sacrifice clarity for conciseness, and this is one of those acceptable instances.

In conclusion, this tossup sucks. Less experienced high school writers often produce even more math tossups of this quality in their sets. Either HSAPQ has bad writers and editors, or good writers and editors with average knowledge of math (Daniel's model math tossup writer) can produce atrocious math tossups.

First of all, I'm not sure how, even in ideal conditions, one tossup from over a year ago can prove anything. Even passing that over, though, it doesn't provide evidence for anything except "bad math tossups happen sometimes." As I understand it, you and Daniel are debating what kind of writer can best produce math tossups, both of you accepting that they, like questions in every other category, are often executed poorly. Unless you can show that this tossup was written by an otherwise good editor without much grounding in math, it proves nothing for your case.

[magin]

I probably could find less than desireable questions in a number of categories. If you found this question poor, give some feedback to the editors who were working on it

I heartily endorse this advice. The most practical way I've seen to improve writing has been to clearly demonstrate why a clue has problems and to contrast it with a better clue, explaining why that clue is better. People want to write the best questions they can, and if your advice is sound, most writers will try to incorporate it.

If it turns out that most current math questions aren't particularly well-written, I also agree with Mike that I don't see why you'd want to see more of them in quizbowl.

[jonah]

If it turns out that most current math questions aren't particularly well-written, I also agree with Mike that I don't see why you'd want to see more of them in quizbowl.

Because they can be written well, they should be written well, and there are people who can write good questions and want to do so (to the point that there are more good math questions than there currently are bad math questions, which is not just a single case in an HSAPQ set from last year).

[t-bar]

de Gua's theorem is only a thing on mathworld and wikipedia. Pythagoras knew about de Gua's theorem, but didn't bother to name it. It literally consists of applying the Pythagorean theorem twice, and any mathematician would call it "Using the Pythagorean theorem twice." Mathworld is actually a horrible source to find out what is notable in math. It's about as accurate as wikipedia, except it has bizzarely little information on some notable topics and contains huge amounts of information on some unimportant topics.

I don't want to wade too deep into this discussion, but I think you may be conflating de Gua's theorem with simply "computing the length of a space diagonal." The latter is, in fact, just two applications of the Pythagorean theorem, but de Gua's theorem is concerned with areas of faces of a tetrahedron. In a little browsing around the internet, I couldn't find any proof that just used the Pythagorean theorem; the one found here, which is fairly straightforward, uses Heron's formula.

To me, the fact that the Pythagorean theorem holds in higher dimensions, as described by de Gua's theorem or papers like this one, seems like an interesting fact that one wouldn't necessarily learn about in the classroom, or while preparing for a math contest, or whatever, but still something that an intellectually curious individual might run across and be able to buzz on. While your critiques of some of the other clues in that tossup are warranted, I think your furor over this one is a little misguided.

[Charles Martel]

Stephen, you're right, I didn't look close enough at what de Gua's theorem was. I believed the theorem was "computing the length of a space diagonal", but in fact it was an interesting lead-in, so this complaint was incorrect.

To begin with, this was not HSAPQ's last ACF set. HSAPQ continues to produce ACF sets to this day. Secondly, never in this entire thread have I explicitly stated that even good editors or writers always produce great questions, just that, on average, they will produce better questions in any given subject area. Until you can produce a wealth of evidence to undermine that claim, in other words one TU, just as it never does, isn't going to cut it, I am going to chose that proven editor or writer over some math lover. Also it is possible that a not so great writer produced that question and that it then got through the editing cracks, HSAPQ isn't perfect.

I said "HSAPQ's last ACF-style site on their website, which it is, since they haven't put their regular season sets from this year on their site yet. I used it out of convenience.

"Most" math questions are bad is an exaggeration. But even in some high school sets that are otherwise good, the percentage of bad questions often approaches 50%. There is indeed a wealth of evidence (See: IMSANITY 2, LIST III) that lots of math can be written and still be good.

IMSANITY 1 Math was too hard for quizbowl today. However, much of this was due to the fact that most of the answer lines had never come up in quizbowl before. In 5 years, I believe that the math canon will have expanded to a reasonable size where these questions will seem less difficult. Also, picking examples of bad IMSANITY 1 CS questions is different from picking examples of bad HSAPQ questions because I am examining 1/3 of the HSAPQ math tossups, while you're looking at 1/36 of the IMSANITY 1 Math tossups (Also, we've separated CS by this point, which we really only put into math as a packetizing convenience in the first place. The difference between Math and CS is important). To defend a particular example, the "23" tossup did not have too steep of a difficulty cliff since the clue before 1+11*2 was essentially asking 4 factorial minues 1.

Finally, the writer of IMSANITY 1 Math had little experience with playing/coaching quizbowl, and no experience whatsoever with writing quizbowl questions. A writer of this type produced better math questions than most of the math questions written by experienced writers with average math knowledge. If you can get writers with decent writing knowledge and lots of math knowledge (such as the IMSANITY 2 and LIST III writers), or a writer with lots of math knowledge and quizbowl writing knowledge (Jonah Greenthal), the math questions would be far superior to most of the ones being written in quizbowl today.

EDIT: Meant IMSANITY 2 at the end, not IMSANITY 1.

[Mewto55555]

"Most" math questions are bad is an exaggeration. But even in some high school sets that are otherwise good, the percentage of bad questions often approaches 50%. There is indeed a wealth of evidence (See: IMSANITY 2, LIST III) that lots of math can be written and still be good.

I really hope you don't know what LIST III looks like!

Also, I completely don't understand the argument. If no one can write good math except for a small handful of people who live in the northern part of the Midwest, why should we expand it everywhere? If we're cherry-picking questions here, we could look at IMSAnity questions like

This country is home to the Miklos Schweitzer Competition, a 10-day mathematics
contest for undergraduates, which is sponsored by the Janos Bolyai society.
With the exception of the USSR and China, this country has won the International
Mathematics Olympiad more than any other. This country's eponymous
algorithm was developed by Kuhn to solve the assignment problem. One mathematician
from this country worked with Morganstern to write * Theory of Games
and Economic Behavior. In addition to John von Neumann, this country is home to a mathematician
with a namesake distance measuring collaboration. FTP, name this European
country, the home of Paul Erdos.

and spend lots of time asking real mathematicians how many of them know things about the Miklos Schweitzer contest (ANSWER: no one who hasn't gone to the AoPS Contest Resources page or lived in Hungary). Every category is going to produce some bad questions if inexperienced people are writing/editing (or even experienced ones!) regardless of where they go to school. Demanding more math in every set is not going to solve this problem; people will be forced to choose stupid answers to expand the canon, or write bad questions on canonical things. Enough sets are bad enough as is; demanding that generic terrible house-write X add more math than they are capable of writing will only make it worse.

Basically, I don't buy the argument chain "HSAPQ/others suck at writing math" (even if that is true!) ---> "We need more people writing math so everyone gets more practice writing math" ---> "Let's make games 24/24"!



Also, as an aside, Adam, your complaint that "math questions in quizbowl bear no resemblance at all to what math is really like, [and] fail to reward any sort of real knowledge in mathematics," strikes me as rather silly, seeing as the experience LIST and IMSA writers share is not competence at "real math" but at contest math, and our sets pretty clearly show this. If your interest is "real math", your chief complaint with math should be "WHAT IS THIS EUCLIDEAN GEOMETRY DOING IN MY QUIZBOWL SET??!!?!?" The "realness" is pretty silly of an argument in and of itself as well, as many other categories suffer from the same problem.

[Matt Weiner]

I will be posting the good news from HSAPQ later tonight. Suffice to say for now that we agree that there should be more math in high school quizbowl than there has been in past HSAPQ sets, and that we don't want to use weak clues of any kind so we welcome feedback such as the above regarding the Pythagorean theorem tossup. Having said that, I want to emphasize that both I personally and HSAPQ as a body strongly disagree with the notion that any innappropriately hard answer line or topic can be "made easier" by asking about it frequently. That's the fallacy known as "the canon" and it is not a solid basis for making decisions about what subjects to write on.

[Smuttynose Island]

To try to better get my point across and perhaps make my ideas clear, I've provided a short explanation and a long explanation of what I'm trying to say for several of my points in this post.

"Most" math questions are bad is an exaggeration. But even in some high school sets that are otherwise good, the percentage of bad questions often approaches 50%. There is indeed a wealth of evidence (See: IMSANITY 2, LIST III) that lots of math can be written and still be good.

SHORT: WHERE'S THE BEEF?

LONG: You have yet to produce a significant wealth of evidence that demonstrates that 50%, or anything near that, of math questions that are produced by otherwise good writers and editors are bad. Throwing random numbers out there without empirical evidence really has not place in any sort of rational discussion. Also citing a set (IMSANITY II and really LIST III, as this year's LIST was LIST II) that no one except for the producers of said set have seen as evidence that good math questions can be written is also a terrible way to go about proving a point and should not be used in a rational discussion.

Finally, the writer of IMSANITY 1 Math had little experience with playing/coaching quizbowl, and no experience whatsoever with writing quizbowl questions. A writer of this type produced better math questions than most of the math questions written by experienced writers with average math knowledge

SHORT: SHOW ME THE MONEY!

LONG: Also you offer no real, saying "This set had good math," because the people who wrote it think that it is good does not consitute valid evidence, evidence that the math in IMSANITY I was better than the average math produced by good editors.

Let's look at the first math question that I found in last year's IMSANITY:

The \"wisted" this is a 3-dimensional parametric curve. Casus irreducibilis refers
to the situation when the roots of a polynomial of this type are all real but
require the use of complex numbers to solve for. Their roots can be found
with * Cardano's formula, but the fact that the roots tend to not be constructible renders
unsolvable two of the three problems of ancient Greek geometry, including trisecting an
angle. Polynomials of this type have exactly one in
ection point and have no maximum or
minimum. FTP, give this adjective describing things with degree 3.
ANSWER: cubic (prompt on \degree 3" before the giveaway)

SHORT: TOO COOL FOR SCHOOL!

LONG: The answerline for this question is fine. Almost anyone, except for maybe some freshman, should know what a "cubic" function is, therefore, if this question has any problems with it it is not going to be for the reason that you mentioned (i.e. the answerline is too hard). That being said, this question does have some major accessibility issues.

You claim that Math should have a greater representation in a QB round mainly because it is taught to everyone. This is a point that I don't dispute and I do genuinely believe that there is more room for Math in QB; however, this question is not what one would expect from someone working under that belief. That is because this question uses exactly two lines of clues that I'd reasonably expect a HS student to learn in math, both coming at the end, and the first one relies on AP Calculus knowledge, which most students simply do not have. If I was writing a question on George Washington and did such a thing people would scream at me for writing what amounts to an inaccessible TU on George Washington and would label that question as "bad," the same goes for this one. Just to be clear, no amount of desired "cannon expansion" will make this TU difficulty appropriate as using similar principles to write a question in any other category would produce a similarly bad question. Now is this a better TU than the terrible one that you produced? Yes, but I would never categorize it as "good."

Here is another math question from the same packet:

This is the smallest number of people needed to guarantee at least a 50 percent
chance that some two will share the same birthday. At the 1900 International
Congress of Mathematicians, David Hilbert set forth this many problems as a
challenge to twentieth century mathematics and Book I of The Elements begins
with this many basic definitions, including \point" and \line". Excluding the
* initial arrangement, there are this many ways to reorder four books on a shelf. Itself a
Germain prime, FTP, name this number which proves that 11 is a Germain prime on account
of it exceeding the double of 11 by 1.
ANSWER: 23

SHORT: RINSE AND REPEAT!

LONG: To begin with, this question shares, to a greater extent, the problem that this TU had in the Once more this TU is significantly harder than any appropriate HS difficulty question should be. This TU uses two clues that really anyone taking math in HS will know, I'm discounting the first clue as, although it is probably used as an example when people are teaching probability hardly anyone will remember it. Your giveaway suffers the problem that it is very difficult to parse at QB speed as you took a seemingly simple concept that could be written as "For 10 points, name this number that is equal to 11 times 2 plus one" and said "exceeding the double of 11 by 1," which is further complicated by the Germain prime junk that you muked the rest of the giveaway with. This question is made further difficult to parse as you add in superflous clues such as "including point and line," which in no way help a player answer the question. With the exception the inaccessibility issue this question's greatest problem is that half of it doesn't even test actual math knowledge. Instead you ask for the number problems that David Hilbert, as if HSers learn about Hilbert's problems in a classroom setting or really more than a tiny percentage of them learn about them at all (when I say this I'm implying that it is less than the percentage that you'd like to have buzzing in on a second line clue), set forth. You then go on to ask about the number of definitions that Euclid put forth in Book 1 of The Elements, as if the number of definitions that Euclid used is really that important to understanding Euclidean geometry (what is important is the definitions themselves). If you don't understand why using those clues are frowned upon then think of it as it applies to different categories. I'd be lambasted if, in a TU on The Old Man in the Sea, I used, as a clue, "This book was published in 1952." That clue in no way tests "important" literary knowledge on The Old Man and the Sea.The only thing that makes the clues in the TU on the number 23 better is that they are uniquely identifying.

If you can get writers with decent writing knowledge and lots of math knowledge (such as the IMSANITY 1 and LIST III writers),

SHORT: MAX ROCKS MY QUESTION WRITING SOCKS!

LONG: LIST II has a lot of good math questions in it and that is partially because Max Schindler is very good at math, but, and I'll say this again and I think that he'd agree with me on this point, the main reason as to why LIST II had good math is not because of his vast knowledge of math, but rather because he is a very good editor and he has good writers helping him out, something that he has demonstrated by producing good questions across all categories. In other words, LIST II really doesn't support your claim as Max Schindler has much more writing knowledge than what most would classify as "decent."

or a writer with lots of math knowledge and quizbowl writing knowledge (Jonah Greenthal), the math questions would be far superior to most of the ones being written in quizbowl today.

No one contests this, in fact this is pretty much just a stronger version of what I am saying (You've added the condition that they have a lot of math knowledge which of course helps. I even said this earlier). If this was your original position on the matter than you should have said that then contested my stance on the issue.

[Charles Martel]

To try to better get my point across and perhaps make my ideas clear, I've provided a short explanation and a long explanation of what I'm trying to say for several of my points in this post.

"Most" math questions are bad is an exaggeration. But even in some high school sets that are otherwise good, the percentage of bad questions often approaches 50%. There is indeed a wealth of evidence (See: IMSANITY 2, LIST III) that lots of math can be written and still be good.

SHORT: WHERE'S THE BEEF?

LONG: You have yet to produce a significant wealth of evidence that demonstrates that 50%, or anything near that, of math questions that are produced by otherwise good writers and editors are bad. Throwing random numbers out there without empirical evidence really has not place in any sort of rational discussion. Also citing a set (IMSANITY II and really LIST III, as this year's LIST was LIST II) that no one except for the producers of said set have seen as evidence that good math questions can be written is also a terrible way to go about proving a point and should not be used in a rational discussion.

HSAPQ sets contain 3 math. I looked up the other two, and one of them is good, and one of them is half good. That's 50% overall for the set. It's not worth my time to go dig up every set out there, find the 3 or 4 math tossups, judge them, and report how many are good. You are correct that LIST and IMSANITY 2 have not yet been released, but the math in those sets the authors have been proud of, and it has been praised by those present for the most part. If you find someone knowledgeable in quizbowl and math with lots of time on their hands, they could dig up the appropriate evidence for you.

Finally, the writer of IMSANITY 1 Math had little experience with playing/coaching quizbowl, and no experience whatsoever with writing quizbowl questions. A writer of this type produced better math questions than most of the math questions written by experienced writers with average math knowledge

SHORT: SHOW ME THE MONEY!

LONG: Also you offer no real, saying "This set had good math," because the people who wrote it think that it is good does not consitute valid evidence, evidence that the math in IMSANITY I was better than the average math produced by good editors.

Let's look at the first math question that I found in last year's IMSANITY:

The \"wisted" this is a 3-dimensional parametric curve. Casus irreducibilis refers
to the situation when the roots of a polynomial of this type are all real but
require the use of complex numbers to solve for. Their roots can be found
with * Cardano's formula, but the fact that the roots tend to not be constructible renders
unsolvable two of the three problems of ancient Greek geometry, including trisecting an
angle. Polynomials of this type have exactly one in
ection point and have no maximum or
minimum. FTP, give this adjective describing things with degree 3.
ANSWER: cubic (prompt on \degree 3" before the giveaway)

SHORT: TOO COOL FOR SCHOOL!

LONG: The answerline for this question is fine. Almost anyone, except for maybe some freshman, should know what a "cubic" function is, therefore, if this question has any problems with it it is not going to be for the reason that you mentioned (i.e. the answerline is too hard). That being said, this question does have some major accessibility issues.

You claim that Math should have a greater representation in a QB round mainly because it is taught to everyone. This is a point that I don't dispute and I do genuinely believe that there is more room for Math in QB; however, this question is not what one would expect from someone working under that belief. That is because this question uses exactly two lines of clues that I'd reasonably expect a HS student to learn in math, both coming at the end, and the first one relies on AP Calculus knowledge, which most students simply do not have. If I was writing a question on George Washington and did such a thing people would scream at me for writing what amounts to an inaccessible TU on George Washington and would label that question as "bad," the same goes for this one. Just to be clear, no amount of desired "cannon expansion" will make this TU difficulty appropriate as using similar principles to write a question in any other category would produce a similarly bad question. Now is this a better TU than the terrible one that you produced? Yes, but I would never categorize it as "good."

I DO NOT claim that math should have a greater representation in quizbowl because it is taught to everyone. It should have a greater representation in quizbowl because of its importance. It will have a high conversion rate because it is taught in school.

Yes, this IMSANITY 1 tossup was too difficult, because the writer overestimated what high schoolers knew. It was pyramidal and didn't contain any difficulty cliffs, but the clues were just too difficult for high schoolers. IMSANITY 2 and the most recent LIST were very good at keeping difficult under control, and future tournament could write 1/1 while doing the same.

Here is another math question from the same packet:

This is the smallest number of people needed to guarantee at least a 50 percent
chance that some two will share the same birthday. At the 1900 International
Congress of Mathematicians, David Hilbert set forth this many problems as a
challenge to twentieth century mathematics and Book I of The Elements begins
with this many basic definitions, including \point" and \line". Excluding the
* initial arrangement, there are this many ways to reorder four books on a shelf. Itself a
Germain prime, FTP, name this number which proves that 11 is a Germain prime on account
of it exceeding the double of 11 by 1.
ANSWER: 23

SHORT: RINSE AND REPEAT!

LONG: To begin with, this question shares, to a greater extent, the problem that this TU had in the Once more this TU is significantly harder than any appropriate HS difficulty question should be. This TU uses two clues that really anyone taking math in HS will know, I'm discounting the first clue as, although it is probably used as an example when people are teaching probability hardly anyone will remember it. Your giveaway suffers the problem that it is very difficult to parse at QB speed as you took a seemingly simple concept that could be written as "For 10 points, name this number that is equal to 11 times 2 plus one" and said "exceeding the double of 11 by 1," which is further complicated by the Germain prime junk that you muked the rest of the giveaway with. This question is made further difficult to parse as you add in superflous clues such as "including point and line," which in no way help a player answer the question. With the exception the inaccessibility issue this question's greatest problem is that half of it doesn't even test actual math knowledge. Instead you ask for the number problems that David Hilbert, as if HSers learn about Hilbert's problems in a classroom setting or really more than a tiny percentage of them learn about them at all (when I say this I'm implying that it is less than the percentage that you'd like to have buzzing in on a second line clue), set forth. You then go on to ask about the number of definitions that Euclid put forth in Book 1 of The Elements, as if the number of definitions that Euclid used is really that important to understanding Euclidean geometry (what is important is the definitions themselves). If you don't understand why using those clues are frowned upon then think of it as it applies to different categories. I'd be lambasted if, in a TU on The Old Man in the Sea, I used, as a clue, "This book was published in 1952." That clue in no way tests "important" literary knowledge on The Old Man and the Sea.The only thing that makes the clues in the TU on the number 23 better is that they are uniquely identifying.

Once again, the early clues were probably a bit too difficult for high school quizbowl, but less than one would imagine. Hilbert's 23 problems are well known among mathematicians, and is a surprisingly buzzable clue, and while asking this question to friends who play quizbowl at different schools (who admittedly know more math that most quizbowlers), most of them buzzed on that clue. The clue about the number of definitions in the Elements is similar to how a literature work would give clues about details in works. It's not important knowledge, but it will be learned in the process of learning important knowledge about it. In some sense, it makes a good clue because knowing the number of definitions is highly correlated with knowing about the Elements.

The only valid criticism of this questions is that despite having decent final conversion, a good last two clues, and entirely uniquely identifying clues, the first few clues were too hard. This is one of the most forgiveable mistakes to make in question writing, and I would this "23" tossup is still better than a decent percentage of the math questions I hear at tournaments.

If you can get writers with decent writing knowledge and lots of math knowledge (such as the IMSANITY 1 and LIST III writers),

SHORT: MAX ROCKS MY QUESTION WRITING SOCKS!

LONG: LIST II has a lot of good math questions in it and that is partially because Max Schindler is very good at math, but, and I'll say this again and I think that he'd agree with me on this point, the main reason as to why LIST II had good math is not because of his vast knowledge of math, but rather because he is a very good editor and he has good writers helping him out, something that he has demonstrated by producing good questions across all categories. In other words, LIST II really doesn't support your claim as Max Schindler has much more writing knowledge than what most would classify as "decent."

Are you seriously arguing that Max isn't as good at math as he is at question writing? Max went to the Math Olympiad Summer Program, something which I haven't been able to achieve despite what I would consider good math knowledge. Anyone who goes to MOP automatically knows quite a bit about math. He has thousands of intelligent posts on the AoPS forums solving problems. I just asked a MOPer what they think of the idea that Max Schindler is average at math and he literally laughed. Max knows a lot of real mathematics and saying that he doesn't is just wrong. On the other hand, this is the second tournament that Max has written, so even though LIST II was a good set, he clearly knows a lot more about math than he does about question writing.

or a writer with lots of math knowledge and quizbowl writing knowledge (Jonah Greenthal), the math questions would be far superior to most of the ones being written in quizbowl today.

No one contests this, in fact this is pretty much just a stronger version of what I am saying (You've added the condition that they have a lot of math knowledge which of course helps. I even said this earlier). If this was your original position on the matter than you should have said that then contested my stance on the issue.

I'm also saying that average writers with lots of math knowledge will produce better questions than good writers with average math knowledge.


I'm not writing a thesis defense here. I'm not going to respond to any more requests to show even more evidence that significant percentages of quizbowl math questions are bad, or any more cherrypicked examples from a set written by inexperienced writers that contains 36 tossups to choose from. Most quizbowlers who know a lot about math would agree that quizbowl math has a long way to go, and it's not even possible to honor both types of requests to "give more evidence" and "stop cherrypicking examples." Stop making arguments on issues where you know you're wrong, just because no one has yet made the counterargument. Some people in this thread are asserting that there are no good math questions, some people are asserting that there are no good math questions, and some people are asserting both!

[Ukonvasara]

Are you seriously arguing that Max isn't as good at math as he is at question writing?

Pretty sure what he's actually arguing is that Max's skills as a question writer have more bearing on his ability to write good (math) questions than do his mathematics skills in the abstract.

or any more cherrypicked examples from a set written by inexperienced writers that contains 36 tossups to choose from.

You're going to have to pick an argument here--you can't hold something up as a paragon of question-writing with one hand and then explain away all its faults with the other.

[Cheynem]

As a moderator, I would gently warn people that saying things like "stop arguing ___" is not allowed.

[Charles Martel]

Are you seriously arguing that Max isn't as good at math as he is at question writing?

Pretty sure what he's actually arguing is that Max's skills as a question writer have more bearing on his ability to write good (math) questions than do his mathematics skills in the abstract.

Yes. But, there is heavy evidence that Max has a lot of mathematics skills, and not a lot to suggest that he has superb question-writing skills. Maybe Max and Prince are both really good writers, in which case there would be no examples of writers with decent question-writing skill and lots of mathematics knowledge.

or any more cherrypicked examples from a set written by inexperienced writers that contains 36 tossups to choose from.

You're going to have to pick an argument here--you can't hold something up as a paragon of question-writing with one hand and then explain away all its faults with the other.

I'm not holding up IMSANITY 1 as a paragon of question-writing. I'm saying that IMSANITY 1 is an example of sub-par question writing by a writer who knew a lot about math, and it turned out better than most math in quizbowl. I could go through the tossups, and show you how almost all of the flaws in mathematics questions resulted from it being slightly too difficult in terms of clue selection. However, I'm telling people that there will be no more responses to anyone who picks an example of an IMSANITY 1 tossup and criticizes it, because I don't have the time to respond to every one of those.

[SirT]

I'm not writing a thesis defense here. I'm not going to respond to any more requests to show even more evidence that significant percentages of quizbowl math questions are bad, or any more cherrypicked examples from a set written by inexperienced writers that contains 36 tossups to choose from. Most quizbowlers who know a lot about math would agree that quizbowl math has a long way to go, and it's not even possible to honor both types of requests to "give more evidence" and "stop cherrypicking examples." Stop making arguments on issues where you know you're wrong, just because no one has yet made the counterargument. Some people in this thread are asserting that there are no good math questions, some people are asserting that there are no good math questions, and some people are asserting both!

Look, those aren't cherry-picked examples. All I did was go through the first two rounds and select all the Math tossups. All Daniel did was open the first round. If we were cherry-picking, there are plenty of better examples than the ones chosen (Max's cherry-picked question being a perfect example).

I'm not sure what the last sentence means, but no one in this thread is saying there are no good math questions, so I'm not sure where that comes from. I'm also unsure what you mean by making arguments on issue where you know you're wrong, would you mind explaining what you mean by that?

Yes. But, there is heavy evidence that Max has a lot of mathematics skills, and not a lot to suggest that he has superb question-writing skills. Maybe Max and Prince are both really good writers, in which case there would be no examples of writers with decent question-writing skill and lots of mathematics knowledge.

That's the most laughable assertion you've made yet. There's plenty of evidence to suggest that Max has a lot of question-writing skill.

I'm not holding up IMSANITY 1 as a paragon of question-writing. I'm saying that IMSANITY 1 is an example of sub-par question writing by a writer who knew a lot about math, and it turned out better than most math in quizbowl. I could go through the tossups, and show you how almost all of the flaws in mathematics questions resulted from it being slightly too difficult in terms of clue selection. However, I'm telling people that there will be no more responses to anyone who picks an example of an IMSANITY 1 tossup and criticizes it, because I don't have the time to respond to every one of those.

I'm not sure why your perspective is so skewed, but this is just completely wrong. This entire tangent has been about how the IMSANITY 1 math [tossups] weren't better than normal--they were very bad, much like the rest of the set! The vast majority of the tossups were too hard and contained huge difficulty cliffs, and plenty of others contained misplaced clues; that's a pretty huge problem that far outshadows whatever YOU think the problems are in other sets.

[Charles Martel]

I'm not writing a thesis defense here. I'm not going to respond to any more requests to show even more evidence that significant percentages of quizbowl math questions are bad, or any more cherrypicked examples from a set written by inexperienced writers that contains 36 tossups to choose from. Most quizbowlers who know a lot about math would agree that quizbowl math has a long way to go, and it's not even possible to honor both types of requests to "give more evidence" and "stop cherrypicking examples." Stop making arguments on issues where you know you're wrong, just because no one has yet made the counterargument. Some people in this thread are asserting that there are no good math questions, some people are asserting that there are no good math questions, and some people are asserting both!

Look, those aren't cherry-picked examples. All I did was go through the first two rounds and select all the Math tossups. All Daniel did was open the first round. If we were cherry-picking, there are plenty of better examples than the ones chosen (Max's cherry-picked question being a perfect example).

It's not really how your selecting them as the fact that there are too many math tossups for me to justify the clue choice and placement on all of them that people ask about.

I'm not sure what the last sentence means, but no one in this thread is saying there are no good math questions, so I'm not sure where that comes from. I'm also unsure what you mean by making arguments on issue where you know you're wrong, would you mind explaining what you mean by that?

Yes. But, there is heavy evidence that Max has a lot of mathematics skills, and not a lot to suggest that he has superb question-writing skills. Maybe Max and Prince are both really good writers, in which case there would be no examples of writers with decent question-writing skill and lots of mathematics knowledge.

That's the most laughable assertion you've made yet. There's plenty of evidence to suggest that Max has a lot of question-writing skill.

There's lots more evidence to suggest that he's very good at math. If you want to say Max is a good question writer, my point still stands that Max was able to distinguish between math clues that matter and math clues that don't because he understood math better, something which people who know less math can't do as well.

I'm not holding up IMSANITY 1 as a paragon of question-writing. I'm saying that IMSANITY 1 is an example of sub-par question writing by a writer who knew a lot about math, and it turned out better than most math in quizbowl. I could go through the tossups, and show you how almost all of the flaws in mathematics questions resulted from it being slightly too difficult in terms of clue selection. However, I'm telling people that there will be no more responses to anyone who picks an example of an IMSANITY 1 tossup and criticizes it, because I don't have the time to respond to every one of those.

I'm not sure why your perspective is so skewed, but this is just completely wrong. This entire tangent has been about how the IMSANITY 1 math [tossups] weren't better than normal--they were very bad, much like the rest of the set! The vast majority of the tossups were too hard and contained huge difficulty cliffs, and plenty of others contained misplaced clues; that's a pretty huge problem that far outshadows whatever YOU think the problems are in other sets.

I would disagree with "majority", but I would agree that many of the tossups in general were horribly flawed. For some reason, I thought "Croesus" was tossupable, and Webster thought that "Red Pony" could be tossed up. The math was an exception, as it was far better than most of the set.

So far, you've failed to demonstrate that IMSANITY 1 Math contained anything other than early clues that sometimes started out too difficult, because only a handful of high schoolers would know those clues. The answer lines were for the most part accessible (a term which means convertable, not the other aspects of a good question that Daniel has tried to infuse into it). I have yet to see a single example of a large difficulty cliff, yet you claim that most of the tossups contained one. The one complaint I haven't seen people making about the math is that clues were misordered, yet you also say that "plenty" contained them. Finally, correctness and uniquely identifying the answer are the two most important aspects of questions, and saying that a difficult lead-in is worse than a blatantly incorrect clue is just wrong. IMSANITY 1 Math was not by any stretch of the imagination bad.

[Angstrom]

I've managed to gather that we're not on 24/24 vs. 20/20 anymore, but I'm not quite sure what the main points in contention are here. Could someone clarify for me? Are we arguing about whether math tossups can be written well, whether most math tossups suck, whether we should have more math tossups, whether we should have better math tossups, or whether Cistercian is underrated?

[Smuttynose Island]

Your TUs did have difficulty cliffs, largely as a result of using too hard clues and then throwing in, in general, a really easy giveaway. Let's reexamine IMSANTIY I's TU on the number 23:

This is the smallest number of people needed to guarantee at least a 50 percent
chance that some two will share the same birthday. At the 1900 International
Congress of Mathematicians, David Hilbert set forth this many problems as a
challenge to twentieth century mathematics and Book I of The Elements begins
with this many basic definitions, including \point" and \line". Excluding the
* initial arrangement, there are this many ways to reorder four books on a shelf. Itself a
Germain prime, FTP, name this number which proves that 11 is a Germain prime on account
of it exceeding the double of 11 by 1.
ANSWER: 23

There is a HUGE difficulty cliff between "name this number which proves that 11 is a Germain prime" and "exceeding the double of 11 by 1." Hardly any HSers know what a Germain prime is. At the HS level a "Germain Prime," just the namedrop even, makes a a pretty good EARLY to early middle clue for a TU on prime numbers, and yet you've managed to include a clue that involves someone knowing what a Germain prime is in your GIVEAWAY right before asking, in a more obtuse manner, what "2*11+1" is. If that's not a difficulty cliff then I'm not sure what is and I forfeit my rights to discuss QB theory.

Now, let's look at that TU on cubic functions:

The \"wisted" this is a 3-dimensional parametric curve. Casus irreducibilis refers
to the situation when the roots of a polynomial of this type are all real but
require the use of complex numbers to solve for. Their roots can be found
with * Cardano's formula, but the fact that the roots tend to not be constructible renders
unsolvable two of the three problems of ancient Greek geometry, including trisecting an
angle. Polynomials of this type have exactly one in
ection point and have no maximum or
minimum. FTP, give this adjective describing things with degree 3.
ANSWER: cubic (prompt on \degree 3" before the giveaway)

You claim that there is no difficulty cliff in this TU, but whenever you go from a topic that is taught in an AP Class to a clue that is a simple as "name this adjective that describes things with degree 3" you have a difficulty cliff. If you don't understand why this is the case it is similar to writing a TU on Louis XIV and going from "This man recognized the King of England by signing the Treaty of Ryswick at the end of the War of the Grand Alliance." to "For 10 points, name this "sun king" of France, the fourteenth of a certain name." Additionally, this TU does in fact contain a non-uniquely identifying clue as many high-order polynomials contain one inflection point and no maximum or minimum (example: f(x)=x^5)

Also would it be possible for a moderator to break off the math discussion from this thread into a seperate thread?