I wrote a (very long) blog post about those viral math problems and am looking for feedback, especially from people who are not convinced that the problem is ambiguous.
It's about a 30min read so thank you in advance if you really take the time to read it, but I think it's worth it if you joined such discussions in the past, but I'm probably biased because I wrote it :)
If you are so sure that you are right and already “know it all”, why bother and even read this? There is no comment section to argue.
I beg to differ. You utter fool! You created a comment section yourself on lemmy and you are clearly wrong about everything!
You take the mean of 1 and 9 which is 4.5!
/j
🤣 I wasn't even sure if I should post it on lemmy. I mainly wrote it so I can post it under other peoples posts that actually are intended to artificially create drama to hopefully show enough people what the actual problems are with those puzzles.
But I probably am a fool and this is not going anywhere because most people won't read a 30min article about those math problems :-)
Actually the correct answer is clearly 0.2609 if you follow the order of operations correctly:
6/2(1+2)
= 6/23
= 0.26
Nah man, distribute the 2.
6/2(1+2)
= 6/2+4
= 3+4
= 7
This is like 4st grayed maff.
I did (skimmed it, at least) and I liked it. 🙃
The answer realistically is determined by where you place implicit multiplication (or "multiplication by juxtaposition") in the order of operations.
Some place it above explicit multiplication and division, meaning it gets done before the division giving you an answer of 1
But if you place it as equal to it's explicit counterparts, then you'd sweep left to right giving you an answer of 9
Since those are both valid interpretations of the order of operations dependent on what field you're in, you're always going to end up with disagreements on questions like these...
But in reality nobody would write an equation like this, and even if they did, there would usually be some kind of context (I.e. units) to guide you as to what the answer should be.
Edit: Just skimmed that article, and it looks like I did remember the last explanation I heard about these correctly. Yay me!
Exactly. With the blog post I try to reach people who already heared that some people say it's ambiguous but either down understand how, or don't believe it. I'm not sure if that will work out because people who "already know the only correct answer" probably won't read a 30min blog post.
Unfortunately these types of viral problems are designed the attract people who think they "know it all", so convincing them that their chosen answer isn't as right as they think it is will always be an uphill challenge
Ackshually, the answer is 4
6÷2*(1+2)
6÷(1+2)*2
6÷(3)*2
2*2
4
You're welcome
Typo in article:
If you are however willing to except the possibility that you are wrong.
Except should be 'accept'.
Not trying to be annoying, but I know people will often find that as a reason to disregard academic arguments.
Thank you very much 🫶. No it's not annoying at all. I'm very grateful not only for the fact that you read the post but also that you took the time to point out issues.
I just fixed it, should be live in a few minutes.
Great write up! The answer is use parentheses or fractions and stop wasting everyone’s time 😅
I tried explaining this to people on facebook in 2010 or so.
"You must be fun at parties!"
Bitch, i dont want to attend your lame ass party where people think they know how math works.
What if the real answer is the friends we made along the way?
This is Facebook we are talking about, what friends? Everyone hates everyone on Facebook
I love that the calculators showing different answers are both from the same manufacturer XD
In the blog post there are even more. Texas Instruments, HP and Canon also have calculators, and some of them show 9 and some 1.
My TI-84 Plus is my holy oracle, I will go with whatever it says.
And then get distracted and play some Doom.
What's especially wild to me is that even the position of "it's ambiguous" gets almost as much pushback as trying to argue that one of them is universally correct.
Last time this came up it was my position that it was ambiguous and needed clarification and had someone accuse me of taking a prescriptive stance and imposing rules contrary to how things were actually being done. How asking a person what they mean or seeking clarification could possibly be prescriptive is beyond me.
Bonus points, the guy telling me I was being prescriptive was arguing vehemently that implicit multiplication having precedence was correct and to do otherwise was wrong, full stop.
👍 That was actually one of the reasons why I wrote this blog post. I wanted to compile a list of points that show as clear as humanity possible that there is no consensus here, even amongst experts.
That probably won't convince everybody but if that won't probably nothing will.
The real lesson here is that clear, unambiguous communication is key.
And just what do you mean by that?
/s
Just write it better.
6/(2(1+2))
Or
(6/2)(1+2)
That's how it works in the real world when you're using real numbers to calculate actual things anyways.
But how would that go viral?
It's hilarious seeing all the genius commenters who didn't read the linked article and are repeating all the exact answers and arguments that the article rebuts :)
Meanwhile programmers will be like, fools, clearly 2(n) is a function 😏
I always hate any viral math post for the simple reason that it gives me PTSD flashbacks to my Real Analysis classes.
The blog post is fine, but could definitely be condensed quite a bit across the board and still effectively make the same points would be my only critique.
At it core Mathematics is the language and practices used in order to communicate numbers to one another and it's always nice to have someone reasonably argue that any ambiguity of communication means that you're not communicating effectively.
The only correct answer is 8008135.
I disagree. Without explicit direction on OOO we have to follow the operators in order.
The parentheses go first. 1+2=3
Then we have 6 ÷2 ×3
Without parentheses around (2×3) we can't do that first. So OOO would be left to right. 9.
In other words, as an engineer with half a PhD, I don't buy strong juxtaposition. That sounds more like laziness than math.
Build two cases, calculate for both, drag both case through the entirety of both problems, get two answers, make a case for both answers, end up with two hypothesis. Easy!
Seems this whole thing is the pedestrian-math-nerd’s equivalent to the pedestrian-grammar-nerd’s arguments on the Oxford comma. At the end of the day it seems mathematical notation is just as flexible as any other facet of written human communication and the real answer is “make things as clear as possible and if there is ambiguity, further clarify what you are trying to communicate.”
I would also add that you shouldn't be using a basic calculator to solve multi part problems. Second, I haven't seen a division sign used in a formal math class since elementary and possibly junior high. These things are almost always written as fractions which makes the logic easier to follow. The entire point of working in convention is so that results are reproducible. The real problem though is that these are not written to educate anyone. They are deliberately written to confuse so that some social media personality can make money from clicks. If someone really wants to practice math skip the click and head over to the Kahn Academy or something similar.
Interesting, I didn't know about strong implicit multiplication. So I would have said the result is 9. All along my studies in France, up to my physics courses at University, all my teachers used weak implicit multiplication. Could be it's the norm in France, or they only use it in math studies at University.
In a scientific context it's actually very rare to run into that issue because divisions are mostly written as fractions which will completely mitigate the issue.
The strong implicit multiplication will only cause ambiguity after a division with inline notation. Once you use fractions the ambiguity vanishes.
In practice you also rarely see implicit multiplications between numbers but mostly between variables or variables and their coefficients.
1 2 + 2 * 6 /
What's the problem?
Also, you forgot my inlaws, one of whom believes the answer is 5.
I really hate the social media discussion about this. And the comments in the past teached me, there are two different ways of learning math in the world.
True, and it's not only about learning math but that there is actually no consensus even amongst experts, about the priority of implicit multiplications (without explicit multiplication sign). In the blog post there are a lot of things that try to show why and how that's the case.
I think this speaks to why I have a total of 5 years of college and no degree.
Starting at about 7th grade, math class is taught to every single American school child as if they're going to grow up to become mathematicians. Formal definitions, proofs, long sets of rules for how you manipulate squiggles to become other squiggles that you're supposed to obey because that's what the book says.
Early my 7th grade year, my teacher wrote a long string of numbers and operators on the board, something like 6 + 4 - 7 * 8 + 3 / 9. Then told us to work this problem and then say what we came up with. This divided us into two groups: Those who hadn't learned Order of Operations on our own time who did (six plus four is ten, minus seven is three, times eight is 24, plus three is 27, divided by nine is three) Three, and who were then told we were wrong and stupid, and those who somehow had, who did (seven times eight is 56, three divided by nine is some tiny fraction...) got a very different number, and were told they were right. Terrible method of teaching, because it alienates the students who need to do the learning right off the bat. And this basically set the tone until I dropped out of college for the second time.
Meanwhile, I'm over in the corner like 