# 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:** 2
**Author:** ![Andy\_L](https://avatars.discourse-cdn.com/v4/letter/a/c67d28/32.png) [@Andy\_L](https://boards.straightdope.com/u/Andy_L)\ **Post date:** [January 8, 2023, 2:59pm UTC](https://boards.straightdope.com/t/why-is-the-answer-to-the-most-annoying-math-puzzle-not-8/977874/21 "2023-01-08T14:59:03Z")
But by thinking about nickels and dollars, it’s obvious that any number less than 1000 is very wrong, so using the nickel/dollar heuristic prevents comes up with a ridiculously wrong answer. Even a question that can’t be answered absolutely correctly can be answered foolishly wrongly - and any mental tool that prevents giving a very wrong answer is useful. ---
**Author:** ![Andy\_L](https://avatars.discourse-cdn.com/v4/letter/a/c67d28/32.png) [@Andy\_L](https://boards.straightdope.com/u/Andy_L)\ **Post date:** [January 8, 2023, 3:06pm UTC](https://boards.straightdope.com/t/why-is-the-answer-to-the-most-annoying-math-puzzle-not-8/977874/22 "2023-01-08T15:06:52Z")
I suspect people would do better with “I put 10 heavy bricks and 4 feathers on one side of the scale and 5 heavy bricks on the other side. How many feathers do I need to put on the second side to balance the scales?” I hope no one would answer “2 feathers” - even though they don’t know how many feathers equals one brick. ---
**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 8, 2023, 3:23pm UTC](https://boards.straightdope.com/t/why-is-the-answer-to-the-most-annoying-math-puzzle-not-8/977874/23 "2023-01-08T15:23:21Z")
> [@griffin1977](#): > > Clearly junction A has some very strange dangerous attribute that means 99.2% of accidents result in serious injuries or death (maybe it’s perched above a sheer cliff face with no barrier, or 99.2% of the vehicles are carrying incredibly dangerous unstable explosives). Indeed, and it is so unrealistic think the only correct response is not to answer, but to ask what on earth is going on here. The ratio of major to minor accidents does not correspond to any sensible model of reality. > [@griffin1977](#): > > _There is a junction A where 2000 major accidents occur and 16 minor accidents. Another junction B has 1000 major accidents occur. How many minor accidents should occur at B for it to be the equivalent of A?_ Since the predominant characteristic of A is its bizarre ratio of major to minor accidents, a plain English interpretation of this ambiguous question is that “equivalent” means “has the same bizarre properties as A” - for example, equivalent in the sense that it is similarly perched on the edge of a cliff. In which case the answer is indeed 8. > [@Novelty\_Bobble](#): > > For you specifically you are missing the fact that this is a question about the modelling of _potential_ junction layouts on the _same_ road. I haven’t watched the video, does he give more context that indicates that by “equivalent” he unambiguously means “equally dangerous as a potential junction configuration at the same location”? ---
**Author:** ![Little\_Nemo](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/little_nemo/32/3120_2.png) [@Little\_Nemo](https://boards.straightdope.com/u/Little_Nemo)\ **Post date:** [January 8, 2023, 3:56pm UTC](https://boards.straightdope.com/t/why-is-the-answer-to-the-most-annoying-math-puzzle-not-8/977874/24 "2023-01-08T15:56:33Z")
> [@Eonwe](#): > > It’s not an annoying math puzzle… it’s unclear language being used as a gotcha. I disagree. It’s not a gotcha unless you define that as a question where some people just answer without thinking. Here’s a similar question: _When I was ten, my brother was half my age. Now I’m twenty. How old is my brother?_ Some people just jump in and say _“Half of twenty is ten. Your brother is ten.”_ That, of course, is not the correct answer. If my brother was half my age when I was ten, then he was five. If I’m now twenty, ten years have gone by. So my brother, who is aging at the same rate as I am, is now fifteen. The same thing occurs with the question in the OP. Some people see that Junction B has half as many major accidents as Junction A. So they jump to the quick answer that Junction B must have half as many minor accidents as Junction A as well. ---
**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 8, 2023, 4:03pm UTC](https://boards.straightdope.com/t/why-is-the-answer-to-the-most-annoying-math-puzzle-not-8/977874/25 "2023-01-08T16:03:19Z")
> [@Riemann](#): > > The ratio of major to minor accidents does not correspond to any sensible model of reality. You think it’s impossible for there to be far more major accidents than minor accidents at a certain spot? > [@Riemann](#): > > I haven’t watched the video, does he give more context that indicates that by “equivalent” he unambiguously means “equally dangerous as a potential junction configuration at the same location”? > [@](#): > > just imagine: the Department for Transport is looking at a road layout and 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. > … > Each of these different road layouts is going to cause a certain number of major and minor road accidents > … > Now what goes here to make these two schemes equivalent? To me, the only reasonble interpretation is “an equivalent number of accidents”; and whatever that means numerically, it does **not** mean a lesser number of both kinds. ---
**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 8, 2023, 4:04pm UTC](https://boards.straightdope.com/t/why-is-the-answer-to-the-most-annoying-math-puzzle-not-8/977874/26 "2023-01-08T16:04:48Z")
> [@Thudlow\_Boink](#): > > You think it’s impossible for there to be far more major accidents than minor accidents at a certain spot? Surely (almost by definition) minor accidents are far more common overall. So a ratio of 100:1 major to minor is very weird and requires explanation. Not _impossible_, but as OP said, is every vehicle carrying unstable explosives or something? > [@Thudlow\_Boink](#): > > To me, the only reasonble interpretation is “an equivalent number of accidents” That would be the reasonable interpretation - IF the bizarre and unexplained ratio of major:minor accidents were not front and center in the framing of the question. ---
**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 8, 2023, 4:07pm UTC](https://boards.straightdope.com/t/why-is-the-answer-to-the-most-annoying-math-puzzle-not-8/977874/27 "2023-01-08T16:07:07Z")
> [@Eonwe](#): > > Even backing out of the math and trying to apply the problem to the real world comparison it tries to address, there seems to be no reason why “how many minor accidents would it take on road B to reach an equivalent amount of harm as road A” is a more correct interpretation than “road A causes this many major and minor accidents. In comparison, road B causes X major accidents. How many minor accidents are likely to occur, given what you know about the relationship between major and minor accidents on road A?” Did you watch the video? I don’t think the context given there allows for your interpretation. (If you don’t want to watch it, I’ve quoted some of the context in Post #25.) ---
**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 8, 2023, 4:13pm UTC](https://boards.straightdope.com/t/why-is-the-answer-to-the-most-annoying-math-puzzle-not-8/977874/28 "2023-01-08T16:13:27Z")
> [@Riemann](#): > > Surely (almost by definition) minor accidents are far more common overall. This looks like denying, or at least questioning, the hypothetical. Surely there must be real-world situations in which failures or accidents are relatively rare, but when they do occur, they are usually serious. And with a different design, those failures might be far more common, but usually more minor when they do occur. ---
**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 8, 2023, 4:19pm UTC](https://boards.straightdope.com/t/why-is-the-answer-to-the-most-annoying-math-puzzle-not-8/977874/29 "2023-01-08T16:19:24Z")
> [@Thudlow\_Boink](#): > > This looks like denying, or at least questioning, the hypothetical. You say that as though questioning a hypothetical is always a mortal sin. If answering a question requires you to use a model of reality, and the hypothetical contains highly atypical characteristics that are left unexplained and _beg_ the question, then asking why the hypothetical is atypical is a more rational approach than guessing. ---
**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 8, 2023, 4:21pm UTC](https://boards.straightdope.com/t/why-is-the-answer-to-the-most-annoying-math-puzzle-not-8/977874/30 "2023-01-08T16:21:34Z")
> [@Riemann](#): > > I haven’t watched the video, does he give more context that indicates that by “equivalent” he unambiguously means “equally dangerous as a potential junction configuration at the same location”? I suggest you have a quick listen to the first minute of the video. He doesn’t use those _exact_ words but he phrases it so that it is heavily implied. Of course this is part of my point. What we _should_ do is take the time to unambigously understand what is being asked and in that universe we ideally come up with similar wording to that which you stated. The point of the example is that we don’t do that nearly often enough and we let our knee-jerk mental maths lead us astray. ---
**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 8, 2023, 4:21pm UTC](https://boards.straightdope.com/t/why-is-the-answer-to-the-most-annoying-math-puzzle-not-8/977874/31 "2023-01-08T16:21:36Z")
> [@Novelty\_Bobble](#): > > The video, and the question as posed, is a really good example of real-world situations that come up time and time again. The point of the video is not to purposefully trick anyone but to shine a light on how we fool ourselves, jump to conclusions, fail to clarify the question etc. I agree, and I like what one of the YouTube commenters said: > [@](#): > > Most students are trained to believe all the information to answer a question is provided in the description. However, this problem is lacking a key piece of information - weighting factors for major and minor accident types. Students need to be taught to perceive when information is missing - that’s as important these days as actually solving the math. In the real world, you are not always given enough information to come up with an exact answer. And in some of those situations, you _can_ come up with a rough estimate, or get an idea of what _kinds_ of answers do or do not make sense. ---
**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 8, 2023, 4:26pm UTC](https://boards.straightdope.com/t/why-is-the-answer-to-the-most-annoying-math-puzzle-not-8/977874/32 "2023-01-08T16:26:32Z")
> [@Thudlow\_Boink](#): > > In the real world, you are not always given enough information to come up with an exact answer. Then the problem should be framed as the kind of situation where it is plausible in real life that it might not be possible to gather more critical relevant information. Analyzing the layout of a junction is not such a situation. ---
**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 8, 2023, 4:27pm UTC](https://boards.straightdope.com/t/why-is-the-answer-to-the-most-annoying-math-puzzle-not-8/977874/33 "2023-01-08T16:27:13Z")
> [@Riemann](#): > > If answering a question requires you to use a model of reality, and the hypothetical contains highly atypical characteristics that are left unexplained and _beg_ the question, then asking why the hypothetical is atypical is a more rational approach than guessing. I don’t disagree. Seeking clarification or asking “Why?” or “What’s going on here?” or “Are you sure those numbers are correct?” are reasonable responses. “8” is not. ---
**Author:** ![Little\_Nemo](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/little_nemo/32/3120_2.png) [@Little\_Nemo](https://boards.straightdope.com/u/Little_Nemo)\ **Post date:** [January 8, 2023, 4:30pm UTC](https://boards.straightdope.com/t/why-is-the-answer-to-the-most-annoying-math-puzzle-not-8/977874/34 "2023-01-08T16:30:13Z")
> [@Riemann](#): > > > [@Thudlow\_Boink](#): > > > > You think it’s impossible for there to be far more major accidents than minor accidents at a certain spot? > > Surely (almost by definition) minor accidents are far more common overall. So a ratio of 100:1 major to minor is very weird and requires explanation. Not _impossible_, but as OP said, is every vehicle carrying unstable explosives or something? We don’t know what ratio is logical without knowing what criteria is used to determine the categories. Perhaps, for example, a “major accident” is defined as one in which at least one vehicle was traveling at fifty miles per hour or faster when the accident occurred. If so, then you would expect that the overwhelming majority of accidents that occur on an expressway would be defined as major accidents. But another location, in a parking lot, will have the majority of accidents occurring there being minor (aka low speed) accidents. But this is a side issue which has no bearing on the answer to the question we’re asked. That question was _“What number of minor accidents would make Location B the equivalent of Location A?”_ We know Location A had two thousand major accidents and sixteen minor accidents. We know Location B had one thousand major accidents and an unknown number of minor accidents. So the question is basically _"If 2000A + 16B = C then what is the correct value of x for 1000A + xB = C?_ ---
**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 8, 2023, 4:36pm UTC](https://boards.straightdope.com/t/why-is-the-answer-to-the-most-annoying-math-puzzle-not-8/977874/35 "2023-01-08T16:36:06Z")
> [@Little\_Nemo](#): > > We know Location A had two thousand major accidents and sixteen minor accidents. We know Location B had one thousand major accidents and an unknown number of minor accidents. You have to be careful with your wording here. It isn’t “Location A and Location B”. They are junction options “A and B” and they are _hypothetical_ models. They haven’t been built and don’t exist. We shouldn’t talk about them as if they do as it muddies the waters even more. ---
**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 8, 2023, 4:43pm UTC](https://boards.straightdope.com/t/why-is-the-answer-to-the-most-annoying-math-puzzle-not-8/977874/36 "2023-01-08T16:43:01Z")
> [@Little\_Nemo](#): > > We don’t know what ratio is logical without knowing what criteria is used to determine the categories. If the question is asking us to apply common sense, any common sense definition of a “minor” traffic incident is something unexceptional that happens more frequently than a “major” incident. Any junction where the number of major accidents (however defined) exceeds minor accidents by a factor of 100 begs explanation - either of the atypical junction, or of the idiosyncratic definition of major and minor. > [@Little\_Nemo](#): > > But this is a side issue which has no bearing on the answer to the question we’re asked. How do we know that unless we ask for an explanation? > [@Little\_Nemo](#): > > That question was _“What number of minor accidents would make Location B the equivalent of Location A?”_ And, again, a perfectly sensible plain English interpretation of “equivalent” is “shares the same atypical and unexplained characteristic as”. Perhaps the questioner himself doesn’t understand why the ratio of major:minor accidents at the first junction is so atypical, and he’s trying to find an _equivalent_ junction with a similar ratio in order to try to see what they have in common. ---
**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 8, 2023, 4:52pm UTC](https://boards.straightdope.com/t/why-is-the-answer-to-the-most-annoying-math-puzzle-not-8/977874/37 "2023-01-08T16:52:56Z")
> [@Riemann](#): > > If the question is asking us to apply common sense, any common sense definition of a “minor” traffic incident is something unexceptional that happens more frequently than a “major” incident. The “definition” given in the video involves the seriousness of the resulting injuries. > [@](#): > > major accidents - this is going to put people in hospital, we’re talking broken bones, you know serious stuff. There’s also a certain number of minor accidents, that might just be like a bit of first aid, you might need to see a doctor, cuts and scrapes, that sort of thing. I don’t find it all that hard to imagine a situation in which any accident has a high chance of being “major”—though I don’t know how realistic my imgainings are. ---
**Author:** ![Little\_Nemo](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/little_nemo/32/3120_2.png) [@Little\_Nemo](https://boards.straightdope.com/u/Little_Nemo)\ **Post date:** [January 8, 2023, 4:57pm UTC](https://boards.straightdope.com/t/why-is-the-answer-to-the-most-annoying-math-puzzle-not-8/977874/38 "2023-01-08T16:57:14Z")
> [@Novelty\_Bobble](#): > > It isn’t “Location A and Location B”. They are junction options “A and B” and they are _hypothetical_ models. They haven’t been built and don’t exist. We shouldn’t talk about them as if they do as it muddies the waters even more. It’s impossible to take mathematics to any level much past simple counting without dealing with abstract and hypothetical situations. ---
**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 8, 2023, 5:00pm UTC](https://boards.straightdope.com/t/why-is-the-answer-to-the-most-annoying-math-puzzle-not-8/977874/39 "2023-01-08T17:00:18Z")
> [@Little\_Nemo](#): > > It’s impossible to take mathematics to any level much past simple counting without dealing with abstract and hypothetical situations. I agree but that’s nothing to do with what I said. If we are still talking about the question in the OP then it is necessary to describe it accurately. Talking about “location A and location B” does not properly describe the OP question. If you are referring to a different question then fine, use your own terminology but it may cause confusion. ---
**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 8, 2023, 5:10pm UTC](https://boards.straightdope.com/t/why-is-the-answer-to-the-most-annoying-math-puzzle-not-8/977874/40 "2023-01-08T17:10:40Z")
Right. The specific wording from the video is > [@](#): > > the Department for Transport is looking at a road layout and 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. I think this is important because it rules out some interpretations of the word “equivalent.” [Previous page](https://boards.straightdope.com/t/why-is-the-answer-to-the-most-annoying-math-puzzle-not-8/977874.md?page=1) [Next page](https://boards.straightdope.com/t/why-is-the-answer-to-the-most-annoying-math-puzzle-not-8/977874.md?page=3)