# 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:** 5
**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, 10:26pm UTC](https://boards.straightdope.com/t/why-is-the-answer-to-the-most-annoying-math-puzzle-not-8/977874/81 "2023-01-08T22:26:56Z")
> [@Riemann](#): > > Exactly the same as me, thanks. What about the opening phrasing makes you think they are talking about two existing roads with different layouts in two different locations? ---
**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, 10:30pm UTC](https://boards.straightdope.com/t/why-is-the-answer-to-the-most-annoying-math-puzzle-not-8/977874/82 "2023-01-08T22:30:08Z")
I was referring to the interpretation of the word “equivalent” as meaning “having the same strange ratio”. That doesn’t depend on whether the layouts are alternative proposals for the same place, or in two different places. ---
**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, 10:33pm UTC](https://boards.straightdope.com/t/why-is-the-answer-to-the-most-annoying-math-puzzle-not-8/977874/83 "2023-01-08T22:33:37Z")
> [@Riemann](#): > > Including the maker of the video, apparently, who first posed the question as “which one is going to cause the fewest accidents”, which implies the exchange rate is 1. Yes, that’s an ambiguous choice of words, even so, taking that at face value there should be very few people putting a figure in that bottom right box that was anything less than 1016. That’s not the case. Clearly that snippet of info slips their minds along with other possible interpretations of of the setup elements as soon as the nice neat numbers appear and a simple solutions occurrs to them that satisfies a very specific definition of “equivalent”. ---
**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, 10:34pm UTC](https://boards.straightdope.com/t/why-is-the-answer-to-the-most-annoying-math-puzzle-not-8/977874/84 "2023-01-08T22:34:44Z")
> [@Novelty\_Bobble](#): > > that’s an ambiguous choice of words That’s not ambiguous it’s plain wrong. His two attempts to pose the question were [1] completely wrong [2] ambiguous ---
**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, 10:36pm UTC](https://boards.straightdope.com/t/why-is-the-answer-to-the-most-annoying-math-puzzle-not-8/977874/85 "2023-01-08T22:36:40Z")
> [@Riemann](#): > > I was referring to the interpretation of the word “equivalent” as meaning “having the same strange ratio”. That doesn’t depend on whether the layouts are alternative proposals for the same place, or in two different places. OK, but I don’t see how that definition of “equivalent” makes good sense when the ultimate intention of the Department of Transport exercise is to choose between two layouts. ---
**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, 10:38pm UTC](https://boards.straightdope.com/t/why-is-the-answer-to-the-most-annoying-math-puzzle-not-8/977874/86 "2023-01-08T22:38:10Z")
> [@Novelty\_Bobble](#): > > I don’t see how that definition of “equivalent” makes good sense when the ultimate intention of the Department of Transport exercise is to choose between two layouts. I have already explained why. In the real world, if a junction layout has a very strange ratio of major to minor accidents, the first thing I would want to do would be to try to understand that. If the explanation were not obvious, I would look at other junction layouts to see how they compare. And since his explanation of the DoT’s objective made no sense in the first place (major and minor accidents carry equal weight), what can you do but ignore _exactly_ what he said (which was plainly wrong) and try to apply common sense to the situation? ---
**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, 10:38pm UTC](https://boards.straightdope.com/t/why-is-the-answer-to-the-most-annoying-math-puzzle-not-8/977874/87 "2023-01-08T22:38:36Z")
> [@Riemann](#): > > That’s not ambiguous it’s plain wrong. > > His two attempts to pose the question were > [1] completely wrong > [2] ambiguous There is definitely ambiguity in there but I don’t think it is completely wrong. If you think so then feel free to write to Tim Harford and tell him that. He’s pretty good at responding to and taking on criticism of what he puts out. ---
**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 8, 2023, 10:39pm UTC](https://boards.straightdope.com/t/why-is-the-answer-to-the-most-annoying-math-puzzle-not-8/977874/88 "2023-01-08T22:39:02Z")
I hate clicking on videos. Fine. First sentence of the set up. Frames as asking number of accidents. Not least harms or least cost. But that mentioned really as almost an aside. Short version he is very unclear on what he is actually asking and flies past the set up. I can see that with lack of a clear question students default to answering questions they have been asked often, simple ratios. And yes 8 is an equivalent ratio. Yeah a poor illustration of the point he is trying to make. ---
**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, 10:39pm UTC](https://boards.straightdope.com/t/why-is-the-answer-to-the-most-annoying-math-puzzle-not-8/977874/89 "2023-01-08T22:39:29Z")
> [@Novelty\_Bobble](#): > > If you think so then feel free to write to Tim Harford and tell him that. And you are also free to write to Tim and tell him you think he’s great. What does that have to do with the price of fish? ---
**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, 10:44pm UTC](https://boards.straightdope.com/t/why-is-the-answer-to-the-most-annoying-math-puzzle-not-8/977874/90 "2023-01-08T22:44:23Z")
> [@Riemann](#): > > I have already explained why. In the real world, if a junction layout has a very strange ratio of major to minor accidents, the first thing I would want to do would be to try to understand that. If the explanation were not obvious, I would look at other junctions to see how they compare. sure, if you are going to fight the hypothetical strange world of these junction options then feel free. I agree that in the real world one of my first responses would be to question the validity of the strange data. I’m accepting the data as given, I’m comfortable that the absurdity of the figures is intentional. ---
**Author:** ![Dr.Strangelove](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/dr.strangelove/32/6613_2.png) [@Dr.Strangelove](https://boards.straightdope.com/u/Dr.Strangelove)\ **Post date:** [January 8, 2023, 10:44pm UTC](https://boards.straightdope.com/t/why-is-the-answer-to-the-most-annoying-math-puzzle-not-8/977874/91 "2023-01-08T22:44:29Z")
> [@Novelty\_Bobble](#): > > It seems fair to infer from that that it is one proposed road with two possible designs in question. I agree that it’s a fair interpretation, just not the only one. You have to read “road layout” in two different ways (proposed road, and possible design) for that to work. But I read it as the DoT looking at road layouts individually, and had two independent cases they were looking at. But even with the assumption of the same location, there’s the question of traffic. Suppose designs A and B are absolutely identical, except one has a tollbooth at one end that limits traffic. In terms of safety, they’re the same (also suppose that the accident rate doesn’t scale with traffic–the cars are flying off a sheer cliff or whatever). In that case, it’s again the ratio that’s important. ---
**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, 10:45pm UTC](https://boards.straightdope.com/t/why-is-the-answer-to-the-most-annoying-math-puzzle-not-8/977874/92 "2023-01-08T22:45:51Z")
> [@Novelty\_Bobble](#): > > fight the hypothetical I’ve already addressed why accusing me of “fighting the hypothetical” _sounds_ like a valid criticism, when in fact it’s not. _Questioning_ a poorly-framed ambiguous hypothetical is the rational way to proceed, not 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, 10:46pm UTC](https://boards.straightdope.com/t/why-is-the-answer-to-the-most-annoying-math-puzzle-not-8/977874/93 "2023-01-08T22:46:56Z")
> [@Riemann](#): > > And you are also free to write to Tim and tell him you think he’s great. What does that have to do with the price of fish? No need for that, it was a genuine suggestion. If you think enough people might find it unclear or willfully ambiguous he’d appreciate your feedback. ---
**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, 10:50pm UTC](https://boards.straightdope.com/t/why-is-the-answer-to-the-most-annoying-math-puzzle-not-8/977874/94 "2023-01-08T22:50:47Z")
> [@Riemann](#): > > I’ve already addressed why accusing me of “fighting the hypothetical” _sounds_ like a valid criticism, when in fact it’s not. _Questioning_ a poorly-framed ambiguous hypothetical is the rational way to proceed, not guessing. OK, you clearly don’t think it is puzzle that is helpful or illuminating. I do. We appear to disagree, that’s not a problem. I can sense you are getting a bit heated here so I’m happy to leave it there. ---
**Author:** ![LSLGuy](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lslguy/32/5813_2.png) [@LSLGuy](https://boards.straightdope.com/u/LSLGuy)\ **Post date:** [January 8, 2023, 10:51pm UTC](https://boards.straightdope.com/t/why-is-the-answer-to-the-most-annoying-math-puzzle-not-8/977874/95 "2023-01-08T22:51:50Z")
The public responding to youtube or facebook quizes are not answering public policy questions. Instead they’re playing a word / numbers game. They’re re-living doing word problems in 4th grade math. It really is no deeper than that. > Billy has 3 oranges. Suzy has 2 more oranges than Billy. How many oranges do Suzy and Billy have together? The reader is entitled to assume the question is no deeper than that. And to apply that level of sophistication to parsing the givens. Now at a meta level, any person choosing to answer one of these silly online quizzes _ought_ to be alert enough to assume that, unlike the 4th grade text, there _will_ be a built-in gotcha someplace, and the obvious answer isn’t the right one. But _oughts_ have very little to do with the average public. My quarrel isn’t with the question as posed by the video. Which I still have not watched and never will. But it is with the video presenter thinking he’s proven any truth greater than “Folks doing 4th grade word problems for entertainment while multitasking 3 other things on their phone aren’t going to try very hard.” ---
**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, 10:57pm UTC](https://boards.straightdope.com/t/why-is-the-answer-to-the-most-annoying-math-puzzle-not-8/977874/96 "2023-01-08T22:57:25Z")
> [@LSLGuy](#): > > My quarrel isn’t with the question as posed by the video. Which I still have not watched and never will. > > But it is with the video presenter thinking If you haven’t watched the video, how do you know what the video presenter was thinking? ---
**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, 11:00pm UTC](https://boards.straightdope.com/t/why-is-the-answer-to-the-most-annoying-math-puzzle-not-8/977874/97 "2023-01-08T23:00:24Z")
> [@Dr.Strangelove](#): > > I agree that it’s a fair interpretation, just not the only one. You have to read “road layout” in two different ways (proposed road, and possible design) for that to work. But I read it as the DoT looking at road layouts individually, and had two independent cases they were looking at. I see far less in the setup that points to existing layouts than to proposed layouts, the “predicted” accidents is another giveaway for me. I agree though that (though I think it is a stretch) other interpretations are possible. > [@Dr.Strangelove](#): > > But even with the assumption of the same location, there’s the question of traffic. Suppose designs A and B are absolutely identical, except one has a tollbooth at one end that limits traffic. In terms of safety, they’re the same (also suppose that the accident rate doesn’t scale with traffic–the cars are flying off a sheer cliff or whatever). In that case, it’s again the ratio that’s important. I’m imagining all of that is taken into account by whatever modelling created the numbers. But ultimately of course, you, I and many others may well dig deep into the question, challenge the assumptions, clarify what is being asked etc. but we may be a self-selecting group of people who would be the same ones saying to the questioner “I can’t answer that without further context, clarification and info”. We aren’t the majority who unthinkingly go for an “obvious” answer. ---
**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, 11:01pm UTC](https://boards.straightdope.com/t/why-is-the-answer-to-the-most-annoying-math-puzzle-not-8/977874/98 "2023-01-08T23:01:49Z")
> [@Novelty\_Bobble](#): > > I can sense you are getting a bit heated here so I’m happy to leave it there. Way to deflect, but I was terse simply because you were repeating a point that had already been made and discussed, ignoring the discussion that had already taken place. ---
**Author:** ![LSLGuy](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lslguy/32/5813_2.png) [@LSLGuy](https://boards.straightdope.com/u/LSLGuy)\ **Post date:** [January 8, 2023, 11:01pm UTC](https://boards.straightdope.com/t/why-is-the-answer-to-the-most-annoying-math-puzzle-not-8/977874/99 "2023-01-08T23:01:57Z")
> [@Thudlow\_Boink](#): > > If you haven’t watched the video, how do you know what the video presenter was thinking? One of the posters here has done a fine job of explaining it over the last 100 posts or so. And I’m sufficiently trusting to take their word for it. ---
**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, 11:05pm UTC](https://boards.straightdope.com/t/why-is-the-answer-to-the-most-annoying-math-puzzle-not-8/977874/100 "2023-01-08T23:05:29Z")
> [@LSLGuy](#): > > My quarrel isn’t with the question as posed by the video. Which I still have not watched and never will. > > But it is with the video presenter thinking he’s proven any truth greater than “Folks doing 4th grade word problems for entertainment while multitasking 3 other things on their phone aren’t going to try very hard.” I don’t think you are being fair to the presenter if you haven’t actually listened to what he has said. The question as given is only really a starting point and as a jumping-off point to the wider concept. Is there a reason why you refuse to watch it? [Previous page](https://boards.straightdope.com/t/why-is-the-answer-to-the-most-annoying-math-puzzle-not-8/977874.md?page=4) [Next page](https://boards.straightdope.com/t/why-is-the-answer-to-the-most-annoying-math-puzzle-not-8/977874.md?page=6)