Quote:
Originally Posted by novox77
Order of operations  Wikipedia, the free encyclopedia
Scroll down to "Gaps in the Standard."
What this section states (or implies) is that if you try to interpret 6÷2(1+2) strictly by the HUMANMADE order of operations, it is ambiguous. The system is not perfect. There are gaps where additional parens are needed to remove ambiguity. But as long as ambiguity exists, it can go multiple ways.
Of course the problem is, most people don't believe that it's ambiguous; they think there must be a correct answer and that their interpretation of PEDMAS is absolutely correct. And in both directions, it's a correct interpretation. That is the definition of ambiguous. That's the reason people are split 50/50 no matter where this question is posed.
It doesn't matter how many PhDs you have and in what field. I'm sure there are superintellects on both camps. The right answer is: don't expect a consensus until you add parentheses to the original problem to make it unambiguous. The problem was designed to exploit the gap in the order of operations.

I believe a distinction should be made; the problem can be written better, but the answer isn't ambiguous.
People in the 1 camp would still have to modify the problem by adding their own independent set of brackets to the equation, in order to arrive at 1, making it look like this:
6÷[2*(1+2)]. < In that specific case, you certainly would solve for the inner set of parenthesis/brackets, and then outward with the second set, multiplying the sum of 1+2 against 2.
As written, but simplified without making any additions or violating rules,
(6)÷(2)(3) or (6)÷(2)*(3)= 9.
Anything else would mean we're placing priority on numbers
outside of parenthesis, or working from right to left.