Put me squarely in the "9" camp please.

You got 3 factorial? Well this just adds a whole new twist. ;)

But yes, it's 9.

You know it!

No, 3 excited.

I did it the way I was taught my entire life, and got 9. I also asked a friend of mine who is working on a Master's degree in mathematics what the solution is and guess what she said? Nine.

lol how did that conversation go? I'd imagine your friend thought you were mocking them, correct?

I don't think so! I just said "hey what's the answer to this problem", and she said 9. She said that when you follow the formula, the equation moves from left to right and no math function takes precedence over another. Basically everything that's been said here already.

Yup! I say it could probably be locked now.

Did you feel like a bit of an idiot as she was explaining it to you, despite her saying everything you already knew?

Again, this adds nothing to the argument, it simply states it differently. Here is where we see to be coming to a disagreement at:

You say that multiplication and division both bear equal precedence between one another, therefore, in a complex equation involving both multiplication and division, one should simply operate from left to right.

My disagreement, which I supported with numerous and equally credible links, says that multiplication ALWAYS takes precedence over division, just as addition ALWAYS takes precedence over subtraction, per the PEMDAS method of operation that was cited in my links, and has been taught to me my entire life, with which Big3 also agreed with.

We both cited sources that are completely conflicting with one another as far as the precedence involved within the order of operations goes. One source says A, the other says B. Both are not correct, but both are not wrong either. As MoonlitSunshine has said, the equation is too ambiguous at this point to be correctly solved using either method of operation.

And I have literally NEVER heard anyone say that they bear the same precedence to one another. I was never taught that in my middle school Pre-Algebra class, Statistics, Algebra, Pre-Calculus, Trigonometry, Calculus I, Calculus II, Calculus III, or the Differential Equations courses that I have completed. I feel that my professors who hold Masters and Doctorates degrees would be a better authority than Google. Again, there seems to be a fundamental difference between the sources that really makes no sense to me.

But if asked to explain why one method of operation would be superior to the other, I would posit this:

Addition is positive, meaning that you are adding something to the number. Subtraction is negative, meaning that you are taking something away from the number. Rather than a left to right interpretation for a method of operation between the two, one should use a Positive>Negative order of operation, as a positive number > a negative number. Do the positive (Addition) first, and the negative (Subtraction) second.

Thusly, Multiplication should be considered the "positive" operation, as the exponents are positive, and Division should be considered the "negative" operation, as it is the inverse of multiplacation, meaning that the exponent is negative.

As all sources have stated, exponents takes precedence over ALL other operations. Per the transitive property, Multiplication (utilizing a positive exponent) therefore takes precedence over Division (utilizing in essence a negative exponent).

With that being said, and Multiplication being the positive operation, and Division being the negative operation, it is easy to come to the result that:

6/2*(1+2) = 6/2*(3) = 6/6 = 1

I remember clearly being taught in my California high school what Burning Down said about P.E.(M./D.)(A./S.) with the left to right. And I made it to AP Calculus and I remember that being taught in a few classes.

I think, oojay, that there are a handful of teachers simply forgetting to tell some generations of students about that important piece of info, that they share precedence and go left to right.

9