Spiro, you touch on something else I remember from my high school days. We were taught to evaluate expressions in simple steps for clarity's sake. I distinctly recall that expression evaluation was basically recursive, with "implicit multiplies" like that always evaluated first in a separate step. I never lost marks by doing it that way. If I were to evaluate your example on a final exam, I would do it something like this.

Suppose a = 1, b = 4, c = 5 [this would be given by the question]

Then:

a + 2b * 3c

= 1 + 2(4) * 3(5)

= 1 + 8 * 15

= 1 + 120

= 121

Applying this same method to the original question, my intuition would have had me go:

6/2(1+2)

= 6/2(3)

= 6/6

= 1

Simply because the 6/2 is not written in orthography that suggests a fraction. Of course, if I had stopped to think about it, meaning that I would treat this with a left-to-right precedence, then I would go:

6/2(1+2)

= (6/2)(3)

= (3)(3)

= 9

Best solutions in my mind:

Personally, my answer would be to punch whoever wrote the equation in the face and tell them that this kind of stupid shit leads to engineering projects failing (possibly at the cost of human lives).

Write the damn equation clearly in the first place.

coupled by

6 / 2 * b is read as "six divided by two times b"
6 / 2b is read as "six over two b"
6/2 * b is read as "six halves times b"
6/2b is read as "six halves b"

On reading the question, my answer is "probably 9 but maybe 1 depending on how they meant it to be interpreted."

Putting the equation into a more graphical form, I believe (and others seem to support) that the first interpretation is correct. But depending on how you read the line, the second one might also be considered correct.

[attachment=26587:mathproblem.PNG]

If I were to write the first one on a keyboard I might, but probably wouldn't, use the equation given: 6/2(1+2). Given my years in the trenches, I learned years ago that to avoid ambiguity you need to write lots of extra parens. Those who lived through the problem of macro abuse know that the entire expression needs its own additional parenthesis around it just in case someone else decides to place another operation adjacent to it. ((6/2)*(1+2))

If I were to write the second style, I would write (6 / (2 * (1+2) ) )

And to be fair many notations suffer from similar communications ambiguity.

If you ask for "the sine of x squared" do you want me to multiply x by x then take the sine? Or take the sine of x and square the result?

And to be fair many notations suffer from similar communications ambiguity.

If you ask for "the sine of x squared" do you want me to multiply x by x then take the sine? Or take the sine of x and square the result?

Not the best example - it's only ambiguous verbally.

The notation is perfectly clear - sin x2 vs sin2 x

And to be fair many notations suffer from similar communications ambiguity.

Not the best example - it's only ambiguous verbally.

Yes, verbally is one of many ways to communicate. Hence it is AN example.

I knew full well that written in standard notation the result is clear. That's why I didn't give the version in math notation.

In mathematics there are standard formats and notations. The puzzle problem of the thread violates the rules for clarity but still has a 'proper' interpretation. The difficulty with so many of these teaser problems is that the puzzle creators intentionally omit or abuse the actual rules in a manner to confuse the reader, much like an IOCCC entry.

That's why I wrote that ChaosEngine had the most correct reply: "Personally, my answer would be to punch whoever wrote the equation in the face and tell them that this kind of stupid shit leads to engineering projects failing (possibly at the cost of human lives)."

The problem is not with the mathematics, the problem is with forming the statement in a misleading or intentionally ambiguous form.

This is all just lazy people shortening expressions so much that they get ambiguous. Its so pointless to insist one or the other was right.

Btw., this option is missing in the pointless poll.

In my view the expression of 6/2(1+2) is poorly formed, and ideally avoided on the ground of clarity and error prevention. Mistakes happen, and when writing something out you should do so in a way that avoids as many potential errors as practically possible. I know some people would argue that it shouldn't matter as only stupid people would get it wrong by not following proper left-right forms, but I would say that only stupid people would try to mix metric and imperial units without converting, and yet we apparently let such people launch stuff into space... Accidents happen, so why not take a little more time and write things in a cleaner notation?

However the implied multiplication trumping standard division and multiplication in ordering is something that I've seen as expected with some engineering formulas. Usually ones from back in the day when everything was being done by hand, and all the engineers I've worked with generally avoid such forms for the reason I stated above.

The formula would have been constant of six divided by two times your variable. 6 over 2x. 2x being the value by which you are dividing six, not the multiplying the variable by six over two. (And usually there would be no reason to write it as (a/b)*x, where a and b are constants because you would have simplified constants when writing out the formula. You're doing all this by hand and reusing that formula in piles of calculations, so you are going to want to get as much work done with it ahead of time as you can unless you have some very good reason not to.)

As a lazy short hand it makes sense within the field, and I've caught myself using it from time to time over the years when scribbling out notes. (I see it as a bad habit.)

This is an example of why having conventions documents are a good thing. Clearly lay out the standards and expectations of communications on a project right at the get go, even if they're the same ones you've been using on all of your projects and are considered 'industry standards'. It is easy to copy and paste old boiler plate content, and one day it might save you or someone else some massive headaches if anyone familiar with some other concept of a standard or convention ever ends up having some involvement with your project.

Btw., this option is missing in the pointless poll.

Other.

This is interesting! In school, I was taught PEMDAS, like many others, with an emphasis on separation of operations. Simply put, Parenthesis (brackets, whatever) are calculated before exponents which is calculated before multiplication which is calculated before division, etc. This was stressed, with the position of values in the expression deemed irrelevant. You read the equation left to right, but you break it up into chunks based on PEMDAS and divide and conquer. This this in mind, the answer can only be one.

Now that I think about it, this makes no sense. Why should multiplication have precedence over division? Why should addition have precedence over subtraction? I agree with whoever wrote PE(M|D)(A|S). That makes far more sense!

No wonder math was my worst subject!

And to be fair many notations suffer from similar communications ambiguity.

Not the best example - it's only ambiguous verbally.

Yes, verbally is one of many ways to communicate. Hence it is AN example.

I knew full well that written in standard notation the result is clear. That's why I didn't give the version in math notation.

"Notation" is not synonymous with "communication".

My point was that your example is not ambiguous because the method of writing is down is ambiguous, but because of how it was expresed in natural language. "Sine of x squared" is ambiguous because in the grammar of English, past participles ("squared") can modify both nouns ("x") and noun phrases ("sine of x") - this ambiguity comes from the language, not the notation.