Math Question - One of Those Silly Ones From Article

[bostonman]

Recently I saw another one of those silly math questions in a news article that emphasize the use of BODMAS in order to solve. Maybe some of you have seen the article, the title will state that adults can't solve this simple math problem.

Having done multiple levels of math for my degree, I've wondered if those "trick" math problems are really ever used.

One example would be something on the idea of 5+(2+3)/2-6.

While this isn't an exact example from a recent news article, is "BODMAS" an actual method in the engineering world or just math playing?

[ataradov]

I don't get the need for acronyms. In Russia we were just told that multiplication and division have higher priority over addition and subtraction and parenthesis are the highest priority. This was enough for everyone to figure it out. It is not like it is so hard you need special mnemonics for that.

Priority of powers was a bit more confusing, but that happens way later in the process and by that time it is not that hard to memorize.

And articles are just stupid clickbait, completely unrelated to anything.

[xrunner]

I don't see how that is a "trick" problem. However, I suppose it might seem that way to some people who don't do math every day. 

[ataradov]

A lot of those "trick" problems include confusing and inconsistent use of * and nothing for multiplication. It would something stupid  like "1+3(5-6)*7" or some other combination.

And the popular one is division without proper parenthesis, like "1*3/5*7". Where it can be interpreted as 1*(3/5)*7 and 1*3/(5*7).

I would put things like this into the same category as EE problems with intentionally confusing resistor networks where the first thing you have to do is redraw the circuit as a sane person would.

[EPAIII]

I think what you need to remember here is that the authors/posters of videos on sites like YouTube are trying to attract viewers because they get PAID for that. So if they can generate a discussion and people view the video and post comments, those authors get PAID. It is all about the $s $s $s $s $s. Or whatever currency they use in their country.

In college my minor was in math. I learned that real mathematicians go to great trouble to formulate their problems and mathematical expressions in a non ambiguous way. They are trying to convey one and only one meaning. That is why you see thing like brackets in their expressions.

On the other hand, these tricksters are trying to formulate their TRICK problems in a manner so that there are two or more ways of evaluating the expression. And they do not tell the reader/viewer which way was intended. This is deliberate and it's purpose is to cause confusion and debate. They are NOT real mathematicians. And frankly, I think they should be ignored. Completely ignored.

...<snip>...

And articles are just stupid clickbait, completely unrelated to anything.

[CatalinaWOW]

These problems are made up to create confusion and draw clicks and comments.  And anyone who creates one in the real world is an idiot.

We have pages of comments on how to make schematics more readable.  We have entire languages (Latex) created to make math equations on paper in a legible format.  Why in this context if you are really trying to communicate an arithmetic problem (or annotate your own work) would you not make every effort to make it clear and obvious?  This is particularly important in an international forum like this because BODMAS does not rule in every location on the earth.  Whitespace and parenthesis are cheap. Use them freely to make the intent clear to everyone, including your future self.

This is not to say that BODMAS doesn't apply in engineering.  If there is no other information available, and if the material you are trying to decipher was generated in an area where BODMAS is taught you should definitely assume that it applies.  And in general when documenting your work (in regions where BODMAS is the standard) you should use BODMAS principals.  But if there is any chance of confusion, clarify your intent as required with parenthesis and the other tools at hand.  Such as breaking the calculation into parts and then combining the intermediate results.

[IanB]

In college my minor was in math. I learned that real mathematicians go to great trouble to formulate their problems and mathematical expressions in a non ambiguous way. They are trying to convey one and only one meaning. That is why you see thing like brackets in their expressions.

I was recently told the same thing by a mathematician. Mathematicians aim to be rigorous and unambiguous. However, engineers tend to be practical and assume others will know what they mean if they use shortcuts or abbreviations.

For instance, engineers may write 1/xy and assume the reader will interpret it as \$\frac{1}{xy}\$ and not as \$\frac{1}{x}y\$

On the other hand, a mathematician would always write 1/(xy) and leave no room for any doubt.

[donlisms]

In the stone ages, I learned the order of operation by... learning the order of operation.  I learned the alphabet by learning the alphabet, though I was young enough that a little sing-song helped.  I learned my multiplication tables by learning them, though I confess there are some (mathematically founded) tricks to help with 9, and 5 and 2, and so on.  Guitar chords. My phone number. I learned to tie my shoes without a story about a rabbit.

I think the best way is to just believe that if you make an effort, you can do hard things.  I think that's being taken away from us.

This reminds me of the recent thread in tricks to learn resistor color codes.  It saddens me; my view of what people are capable of is higher than that, I guess.  We're being dumbed down. 

[Haenk]

It's just built on misleading notation.
So while being funny, it's a pointless discussion, as there is no correct answer at all.

That's also an issue with linguistic expressions. Like this example (in German):
"Komm, wir essen, Opa!"
"Komm, wir essen Opa!"

(roughly translates to "Come, dinner is ready, grandpa!" and "Come, let's eat Grandpa!")
The comma should be a verbal "pause", but that pause is usually ignored.

[wasedadoc]

Animal in nature documentary:  Eats shoots and leaves.
Cowboy in western movie: Eats, shoots and leaves.

He was attacked by a man eating fish.
He was attacked by a man-eating fish.

[TimFox]

In college my minor was in math. I learned that real mathematicians go to great trouble to formulate their problems and mathematical expressions in a non ambiguous way. They are trying to convey one and only one meaning. That is why you see thing like brackets in their expressions.

I was recently told the same thing by a mathematician. Mathematicians aim to be rigorous and unambiguous. However, engineers tend to be practical and assume others will know what they mean if they use shortcuts or abbreviations.

For instance, engineers may write 1/xy and assume the reader will interpret it as \$\frac{1}{xy}\$ and not as \$\frac{1}{x}y\$

On the other hand, a mathematician would always write 1/(xy) and leave no room for any doubt.

My education was in physics, with lots of mathematics on the side.
I learned the conventional order of operations, but I saw no reason not to be careful and use parentheses to avoid possible confusion.
I only needed to know the conventional order in order to read equations done by those less careful than I.
Incidentally, "Polish notation" (well-known in reverse as RPN, found in good calculators) was invented by Łukasiewicz (whose name is hard to pronounce in reverse order, hence the abbreviation RPN) to avoid ambiguity without recourse to parentheses.
I encountered Łukasiewicz' notation in the forward direction in a class on formal logic;  compared with "infix" notation for logical formulae, it also avoids special characters, using only majuscules and miniscules found on a normal typewriter.
https://plato.stanford.edu/entries/lukasiewicz/polish-notation.html
There is an example for a formula in propositional calculus half-way through that citation (which does not copy) that requires 43 characters, including 20 parentheses, in "normal" spelling, but only 23 characters in Łukasiewicz' notation, all of which are "active".

[Nominal Animal]

I like to avoid ambiquities, and tend to use parentheses whenever useful, even when not required.

It is somewhat like including units or dimensions when calculating something.  Most people like to omit the units during calculation, but I find them useful, especially when I end up combining constants or substituting variables with their values; often acts like a "checksum" showing me if I forgot or miscalculated something.  Plus, of course, dimensional analysis is always useful when examining a formula for sanity.

Those "math" questions based on ambiquity of the expression, really annoy me.  I find them dishonest: it is not a math problem that humans do not agree on some corner case rule or another; it is a human problem.

[IanB]

There is an example for a formula in propositional calculus half-way through that citation (which does not copy) that requires 43 characters, including 20 parentheses, in "normal" spelling, but only 23 characters in Łukasiewicz' notation, all of which are "active".

In that example, we have this in infix notation:
$$\big((p \Rightarrow r) \land (q \Rightarrow r)\big) \land \big((p \Rightarrow s) \land (q \Rightarrow s)\big) \Leftrightarrow \big((p \lor q) \Rightarrow (r \land s)\big)$$
And this in prefix notation:
$$EKKCprCqrKCpsCqsCApqKrs$$
However, I would argue that the prefix notation is only readable by a computer. For a human to read it, it still needs parentheses:
$$E \Big(K(K\:Cpr\:Cqr)(K\:Cps\:Cqs)\Big) \Big(C\:Apq\:Krs\Big)$$

[Terry Bites]

Maths jokes never funny. Dont give them a second thought, fill your mind with finer things.

[TimFox]

There is an example for a formula in propositional calculus half-way through that citation (which does not copy) that requires 43 characters, including 20 parentheses, in "normal" spelling, but only 23 characters in Łukasiewicz' notation, all of which are "active".

In that example, we have this in infix notation:
$$\big((p \Rightarrow r) \land (q \Rightarrow r)\big) \land \big((p \Rightarrow s) \land (q \Rightarrow s)\big) \Leftrightarrow \big((p \lor q) \Rightarrow (r \land s)\big)$$
And this in prefix notation:
$$EKKCprCqrKCpsCqsCApqKrs$$
However, I would argue that the prefix notation is only readable by a computer. For a human to read it, it still needs parentheses:
$$E \Big(K(K\:Cpr\:Cqr)(K\:Cps\:Cqs)\Big) \Big(C\:Apq\:Krs\Big)$$

To read the prefix notation, you need to read from the inside out.
Since most natural language is not done that way (e.g., English prose), this notation is not popular, but I learned to read it in that college course.
An advantage, discussed in the article, is that one can determine quickly if the equation is logically correct by counting symbols.
I have used RPN calculators since the 1970s, after I learned that when approaching a problem in front of me that RPN was closer to my thought process than was algebraic.
Algebraic is more popular when looking at an equation written out beforehand.

[gnuarm]

There is an example for a formula in propositional calculus half-way through that citation (which does not copy) that requires 43 characters, including 20 parentheses, in "normal" spelling, but only 23 characters in Łukasiewicz' notation, all of which are "active".

In that example, we have this in infix notation:
$$\big((p \Rightarrow r) \land (q \Rightarrow r)\big) \land \big((p \Rightarrow s) \land (q \Rightarrow s)\big) \Leftrightarrow \big((p \lor q) \Rightarrow (r \land s)\big)$$
And this in prefix notation:
$$EKKCprCqrKCpsCqsCApqKrs$$
However, I would argue that the prefix notation is only readable by a computer. For a human to read it, it still needs parentheses:
$$E \Big(K(K\:Cpr\:Cqr)(K\:Cps\:Cqs)\Big) \Big(C\:Apq\:Krs\Big)$$

I know prefix notation exists, but I've never seen it used.  Postfix is very simple and clear.

It looks to me like your prefix notation is just postfix written in reverse.  So, it should be very simple for anyone to use prefix if they simply read it as postfix, starting from the right hand side.

[TimFox]

Here, “prefix” is equivalent to “Polish” notation, and “postfix” is equivalent to the better-known reverse Polish notation (RPN).

[Infraviolet]

"I've wondered if those "trick" math problems are really ever used"
Usually only by accident, the person writing down an equation was in a rush and didn't think of the order of operations, and then the person reading it interprets it according to the proper rules.

Also sometimes accidents in computer code if one doesn't bracket properly, some compilers use a different O of O to that which is used in written mathematics.

The BODMAS (also BIDMAS with I being for Indices) acronym was used quite a lot in teaching in the UK at multiple levels as a reminder to help when people forgot the order.

I also recall when young I had to remind a teacher of a non-mathematical subject at school about this. He was presenting a formula used in something like geography or sports scoring, "that needs brackets" I said, "you need brackets" came his response. I think he normally only thought of the formula as words describing how to do the calculation "subtract this then divide by that" and never realised how ambigous, or infact plain wrong, it could be when written mathematically left to right.

[TimFox]

Besides "BODMAS", I also learned to nest bracket-like objects as { [ ( ) ] } as a convention for parenthetical statements.

[ledtester]

There is an example for a formula in propositional calculus half-way through that citation (which does not copy) that requires 43 characters, including 20 parentheses, in "normal" spelling, but only 23 characters in Łukasiewicz' notation, all of which are "active".

In that example, we have this in infix notation:
$$\big((p \Rightarrow r) \land (q \Rightarrow r)\big) \land \big((p \Rightarrow s) \land (q \Rightarrow s)\big) \Leftrightarrow \big((p \lor q) \Rightarrow (r \land s)\big)$$
And this in prefix notation:
$$EKKCprCqrKCpsCqsCApqKrs$$
However, I would argue that the prefix notation is only readable by a computer. For a human to read it, it still needs parentheses:
$$E \Big(K(K\:Cpr\:Cqr)(K\:Cps\:Cqs)\Big) \Big(C\:Apq\:Krs\Big)$$

That prefix notation is used in the logic game WFF N'Proof:

https://americanhistory.si.edu/collections/search/object/nmah_694594

[TimFox]

And "WFF 'N Proof" was not a computer game.
"WFF" is an abbreviation for "well-formed formula" in predicate calculus.

[Benta]

Those newspaper "puzzles" using incomplete notation to create MDAS obfuscation bore me. But they always get a rise from the public.

This one's subtler, showing that 2=1 (I'm certain some of you know it already. Refrain from replying and let's see what happens):

[TimFox]

I first encountered that proof in 1964, so I recuse myself from replying.

[Benta]

Yeah, never said it's new.

[TimFox]

It will still be new to some people younger than I.