# Why is the answer to "the most annoying math puzzle" not 8? **URL:** \ **Category:** In My Humble Opinion\ **Created:** [January 8, 2023, 12:14pm UTC](https://boards.straightdope.com/t/why-is-the-answer-to-the-most-annoying-math-puzzle-not-8/977874 "2023-01-08T12:14:25Z")\ **Posts on this page:** 20\ **Page:** 9
**Author:** ![Riemann](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/riemann/32/3133_2.png) [@Riemann](https://boards.straightdope.com/u/Riemann)\ **Post date:** [January 9, 2023, 7:17pm UTC](https://boards.straightdope.com/t/why-is-the-answer-to-the-most-annoying-math-puzzle-not-8/977874/161 "2023-01-09T19:17:36Z")
> [@Chronos](#): > > Like, if this is an 80 MPH road: It’s really, really hard to have a minor accident at 80 MPH. Is it really so hard to have an accident where nobody is seriously injured? Sure, it’s intuitive that a somewhat larger proportion of accidents would be serious at a higher speed, but the ratio given was **100:1**. That would appear to require that everyone is carrying unstable high explosives in their vehicle, or that the junction is perched on the edge of a cliff. It begs explanation. Maybe there _is_ an explanation, but I would call it a far greater cognitive error to fail to recognize that we cannot have any confidence in our model unless we know why this is happening. ---
**Author:** ![Novelty\_Bobble](https://avatars.discourse-cdn.com/v4/letter/n/a3d4f5/32.png) [@Novelty\_Bobble](https://boards.straightdope.com/u/Novelty_Bobble)\ **Post date:** [January 9, 2023, 7:18pm UTC](https://boards.straightdope.com/t/why-is-the-answer-to-the-most-annoying-math-puzzle-not-8/977874/162 "2023-01-09T19:18:57Z")
> [@Riemann](#): > > You are reaching here - they are not bizarre in the same way. no, they are not bizarrre in quite the same way and to the same extent, but there are elements of wierdness and nonsense in all of the questions. All of them have some elements of artifice to a greater or lesser extent. ---
**Author:** ![DSeid](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/dseid/32/20194_2.png) [@DSeid](https://boards.straightdope.com/u/DSeid)\ **Post date:** [January 9, 2023, 7:21pm UTC](https://boards.straightdope.com/t/why-is-the-answer-to-the-most-annoying-math-puzzle-not-8/977874/163 "2023-01-09T19:21:47Z")
I’m not even sure that most who get the CRT ones right are reflecting rather than using a correct approach to begin with. ---
**Author:** ![tullsterx](https://avatars.discourse-cdn.com/v4/letter/t/e9bcb4/32.png) [@tullsterx](https://boards.straightdope.com/u/tullsterx)\ **Post date:** [January 9, 2023, 7:26pm UTC](https://boards.straightdope.com/t/why-is-the-answer-to-the-most-annoying-math-puzzle-not-8/977874/164 "2023-01-09T19:26:53Z")
That’s the way I read it. How many Minor accidents at B to make is AS DANGEROUS as A. That’s what I was thinking. Plus, I have no idea how you came up with 8. Just matching the ratio? I’m thinking it would start with 1016 and go up from there. Anyway. . . ---
**Author:** ![griffin1977](https://avatars.discourse-cdn.com/v4/letter/g/977dab/32.png) [@griffin1977](https://boards.straightdope.com/u/griffin1977)\ **Post date:** [January 9, 2023, 7:29pm UTC](https://boards.straightdope.com/t/why-is-the-answer-to-the-most-annoying-math-puzzle-not-8/977874/165 "2023-01-09T19:29:14Z")
> [@tullsterx](#): > > That’s the way I read it. How many Minor accidents at B to make is AS DANGEROUS as A. That’s what I was thinking. That’s one way to interpret “equivalent”. > [@tullsterx](#): > > Plus, I have no idea how you came up with 8. Just matching the ratio? Yes, and that is a perfectly reasonable way to interpret “equivalent” just a correct as “as dangerous as”. ---
**Author:** ![Thudlow\_Boink](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/thudlow_boink/32/320_2.png) [@Thudlow\_Boink](https://boards.straightdope.com/u/Thudlow_Boink)\ **Post date:** [January 9, 2023, 7:34pm UTC](https://boards.straightdope.com/t/why-is-the-answer-to-the-most-annoying-math-puzzle-not-8/977874/166 "2023-01-09T19:34:14Z")
> [@griffin1977](#): > > Also it sees 2000 major accidents! Even the most insanely dangerous junction wouldn’t see anything like that IRL. That number isn’t given any context (like, 2000 accidents over what time span?); it’s just “predicted to have a certain number of major accidents.” We’re not told what the prediction is based on, but maybe it’s the result of running a computer simulation, simulating the equivalent of many years’ worth of heavy traffic. ---
**Author:** ![tullsterx](https://avatars.discourse-cdn.com/v4/letter/t/e9bcb4/32.png) [@tullsterx](https://boards.straightdope.com/u/tullsterx)\ **Post date:** [January 9, 2023, 7:35pm UTC](https://boards.straightdope.com/t/why-is-the-answer-to-the-most-annoying-math-puzzle-not-8/977874/167 "2023-01-09T19:35:49Z")
Maybe. I work in traffic, so my mind would never go there. I’m concerned with how dangerous the intersection is. ---
**Author:** ![Riemann](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/riemann/32/3133_2.png) [@Riemann](https://boards.straightdope.com/u/Riemann)\ **Post date:** [January 9, 2023, 7:37pm UTC](https://boards.straightdope.com/t/why-is-the-answer-to-the-most-annoying-math-puzzle-not-8/977874/168 "2023-01-09T19:37:37Z")
> [@Thudlow\_Boink](#): > > That number isn’t given any context (like, 2000 accidents over what time span?); it’s just “predicted to have a certain number of major accidents.” We’re not told what the prediction is based on, but maybe it’s the result of running a computer simulation, simulating the equivalent of many years’ worth of heavy traffic. Yup, and I think I would say that if this were a real life situation, giving _any_ answer without investigating the poorly-described circumstances and unexplained data much more fully is very wrong. The greatest cognitive error here would be to fail to recognize that the bizarre 100:1 ratio may imply that your model for how junctions work is completely wrong. So I don’t give much credence to the notion that answering 8 is “more” wrong than any other answer. Planning junction design clearly isn’t an urgent situation where giving an immediate best estimate is necessary. So I think in real life the wrongness of giving _any_ answer overwhelms any dispute about whether one specific answer is more wrong than another one. ---
**Author:** ![Thing.Fish](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/thing.fish/32/9168_2.png) [@Thing.Fish](https://boards.straightdope.com/u/Thing.Fish)\ **Post date:** [January 9, 2023, 8:36pm UTC](https://boards.straightdope.com/t/why-is-the-answer-to-the-most-annoying-math-puzzle-not-8/977874/169 "2023-01-09T20:36:08Z")
I think 8 is a fine answer. The question is ambiguous and admits of two possible interpretations. One is that it is a straightforward algebra problem. The other is that it is obviously impossible to answer because key concepts aren’t adequately defined. I don’t think it’s unreasonable to assume that the questioner probably meant to ask a question that could actually be answered given the information provided. ---
**Author:** ![Thudlow\_Boink](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/thudlow_boink/32/320_2.png) [@Thudlow\_Boink](https://boards.straightdope.com/u/Thudlow_Boink)\ **Post date:** [January 9, 2023, 8:55pm UTC](https://boards.straightdope.com/t/why-is-the-answer-to-the-most-annoying-math-puzzle-not-8/977874/170 "2023-01-09T20:55:21Z")
For those of you who think 8 is a fine answer, what would you say to this: A car dealership is trying to decide between two proposed ad campaigns. Under Campaign A, it is predicted that they would sell 2000 trucks and 16 cars. Under Campaign B, they would sell 1000 trucks. How many cars would they have to sell in order for the two campaigns to be equivalent? ---
**Author:** ![Thing.Fish](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/thing.fish/32/9168_2.png) [@Thing.Fish](https://boards.straightdope.com/u/Thing.Fish)\ **Post date:** [January 9, 2023, 9:01pm UTC](https://boards.straightdope.com/t/why-is-the-answer-to-the-most-annoying-math-puzzle-not-8/977874/171 "2023-01-09T21:01:54Z")
Well, you could look at it as an algebra problem and say the answer is 8. In your example, that does seem intuitively less reasonable than it did in the OP. Or you could say that you can’t answer without knowing the profit margins on trucks and cars, which should already be obvious to anyone with an ounce of common sense. So I guess the answer to the OP depends on whether you think the person asking it is prone to asking obviously stupid questions. In your reformulation, it’s clearer that both possible interpretations of the question are stupid, so you have even less to go on. ---
**Author:** ![Thudlow\_Boink](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/thudlow_boink/32/320_2.png) [@Thudlow\_Boink](https://boards.straightdope.com/u/Thudlow_Boink)\ **Post date:** [January 9, 2023, 9:05pm UTC](https://boards.straightdope.com/t/why-is-the-answer-to-the-most-annoying-math-puzzle-not-8/977874/172 "2023-01-09T21:05:32Z")
> [@Thing.Fish](#): > > Well, you could look at it as an algebra problem and say the answer is 8. I’m not sure what you mean by “look at it as an algebra problem.” Perhaps you mean “a proportion problem”? Which still leaves the question of _why_ one would assume it’s a proportion problem. To me, “look at it as an algebra problem” would mean to solve it by translating it into an algebraic equation. But you’d still have to figure out _what_ equation reflects the situation described. > [@Thing.Fish](#): > > Or you could say that you can’t answer without knowing the profit margins on trucks and cars, which should already be obvious to anyone with an ounce of common sense. Right, and in that sense it matches the original problem. Which could reasonably interpreted as the kind of problem where the point wasn’t to come up with a single number, but to either (1) figure out what _kind_ or _range_ of numbers would make sense as an answer, or (2) figure out what additional information would be needed to arrive at a reasonable answer. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [January 9, 2023, 9:12pm UTC](https://boards.straightdope.com/t/why-is-the-answer-to-the-most-annoying-math-puzzle-not-8/977874/173 "2023-01-09T21:12:46Z")
That does have the weakness that it’s not inherently obvious that a truck sale is more important than a car sale. Trucks on average probably net more profit for the dealer than cars on average, but maybe this dealership sells a lot of high-end sports cars or luxury cars. So it’s not “I don’t know, but it’s at least 1016”, but just “I don’t know”, or at best “I don’t know, but maybe somewhere in the vicinity of 1000”. ---
**Author:** ![Thing.Fish](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/thing.fish/32/9168_2.png) [@Thing.Fish](https://boards.straightdope.com/u/Thing.Fish)\ **Post date:** [January 9, 2023, 9:13pm UTC](https://boards.straightdope.com/t/why-is-the-answer-to-the-most-annoying-math-puzzle-not-8/977874/174 "2023-01-09T21:13:51Z")
I am bad at math terminology. I mean rephrasing it as “what is to 1000 as 16 is to 2000”? As to why you would assume that, I don’t know why it’s intrinsically less plausible than thinking “ah, I am being tested to see if I can identify the fact that there isn’t enough information to answer this question”. In either case, the answer is so trivially obvious that one wonders why anyone would bother asking, so you’d really have to try to use context to determine which answer the questioner was going for. ---
**Author:** ![Riemann](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/riemann/32/3133_2.png) [@Riemann](https://boards.straightdope.com/u/Riemann)\ **Post date:** [January 9, 2023, 9:15pm UTC](https://boards.straightdope.com/t/why-is-the-answer-to-the-most-annoying-math-puzzle-not-8/977874/175 "2023-01-09T21:15:57Z")
> [@Thudlow\_Boink](#): > > A car dealership is trying to decide between two proposed ad campaigns. Under Campaign A, it is predicted that they would sell 2000 trucks and 16 cars. Under Campaign B, they would sell 1000 trucks. How many cars would they have to sell in order for the two campaigns to be equivalent? The data are still unusual, but obviously it’s not implausible that a dealership would specialize in trucks. That’s the key difference here. I suppose the same ambiguity about “equivalent” is there, it could be that the dealership wants to compare campaigns that are “equivalent in targeting”, i.e. targeted in the same manner principally at truck buyers to generate a similar proportion of truck vs car sales. After all, you haven’t said what the two campaigns cost - the second one could cost half as much, it could be an expensive TV campaign vs a cheap radio campaign. But here I think that interpretation seems less likely. And since the metric for a business is obviously money, the more natural interpretation is that the question is probably asking about the total value that each campaign would generate in sales. In real life, I would still check exactly what the question meant. Perhaps this would be a clearer way to present the question intended in the video, but I’m not sure that testing whether people do or do not see ambiguity in the word “equivalent” is suppoed to be the point of a CRT test. Any uncertainty about the answer seems to hinge on that ambiguity. ---
**Author:** ![Thing.Fish](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/thing.fish/32/9168_2.png) [@Thing.Fish](https://boards.straightdope.com/u/Thing.Fish)\ **Post date:** [January 9, 2023, 9:23pm UTC](https://boards.straightdope.com/t/why-is-the-answer-to-the-most-annoying-math-puzzle-not-8/977874/176 "2023-01-09T21:23:40Z")
Yes, I agree. Our knowledge that businesses operate to make money makes the use of “equivalent” in Boink’s example much less ambiguous than that in the OP. ---
**Author:** ![peccavi](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/peccavi/32/388_2.png) [@peccavi](https://boards.straightdope.com/u/peccavi)\ **Post date:** [January 9, 2023, 9:33pm UTC](https://boards.straightdope.com/t/why-is-the-answer-to-the-most-annoying-math-puzzle-not-8/977874/177 "2023-01-09T21:33:48Z")
> [@Thing.Fish](#): > > Yes, I agree. Our knowledge that businesses operate to make money makes the use of “equivalent” in Boink’s example much less ambiguous than that in the OP I don’t know about that. There’s nothing in the term “equivalent” that requires it concern money. Perhaps it the dealership only receives one car for some number of trucks it receives, then the equivalence is going to be a ratio. And even if it does mean money, is equivalence defined in sales, profit, after-sales revenue (maintenance and repair), or other financial measures? In fact, in the real world, using the term “equivalent” with no modifiers or context indicates poor cognitive reasoning power on the part of the questioner. ---
**Author:** ![Riemann](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/riemann/32/3133_2.png) [@Riemann](https://boards.straightdope.com/u/Riemann)\ **Post date:** [January 9, 2023, 9:40pm UTC](https://boards.straightdope.com/t/why-is-the-answer-to-the-most-annoying-math-puzzle-not-8/977874/178 "2023-01-09T21:40:23Z")
> [@Thing.Fish](#): > > Yes, I agree. Just to note that I edited my post quite a bit, and I think you posted “I agree” halfway through. I’m not sure if you actually agree with the way I eventually wrote it! ---
**Author:** ![suranyi](https://avatars.discourse-cdn.com/v4/letter/s/e36b37/32.png) [@suranyi](https://boards.straightdope.com/u/suranyi)\ **Post date:** [January 9, 2023, 9:41pm UTC](https://boards.straightdope.com/t/why-is-the-answer-to-the-most-annoying-math-puzzle-not-8/977874/179 "2023-01-09T21:41:24Z")
Yes, the issue is that the word “equivalent” is undefined, at least the way the OP stated it. (Maybe the video is clearer.). When I saw the problem, I immediately assumed “equivalent” meant “make them have the same ratio”, in which case the answer is indeed 8. It never even occurred to me that it might mean “make them have the same degree of danger” until I started reading this thread. ---
**Author:** ![Thudlow\_Boink](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/thudlow_boink/32/320_2.png) [@Thudlow\_Boink](https://boards.straightdope.com/u/Thudlow_Boink)\ **Post date:** [January 9, 2023, 9:47pm UTC](https://boards.straightdope.com/t/why-is-the-answer-to-the-most-annoying-math-puzzle-not-8/977874/180 "2023-01-09T21:47:59Z")
> [@suranyi](#): > > at least the way the OP stated it. (Maybe the video is clearer.). When I saw the problem, I immediately assumed “equivalent” meant “make them have the same ratio” I don’t think that assumption is as natural the way the problem is stated in the video (“they’ve got two different possibilities for the road layout and they’re trying to figure out which one is going to cause the fewest accidents”) as it is the way the OP reformulated it (“There is a junction A where 2000 major accidents occur and 16 minor accidents. Another junction B has 1000 major accidents occur”). [Previous page](https://boards.straightdope.com/t/why-is-the-answer-to-the-most-annoying-math-puzzle-not-8/977874.md?page=8) [Next page](https://boards.straightdope.com/t/why-is-the-answer-to-the-most-annoying-math-puzzle-not-8/977874.md?page=10)