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 HUMAN-MADE 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 super-intellects 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
Originally Posted by XplosiV
It seems to me that the answer is somewhat split between the simple folk and the math geeks. Ask anyone in the street and they will probably solve the question using left to right. where as ask anyone with some kind of higher education in math, and they will probably use the math parenthesis. Theres not a lot of point 'simplifying' the problem, the problem 'as is' done by a mathematician, using the common laws of math, will simply answer it as 1.
Who can tell me the highest number, that when written in the queens English, consists of only three words?
(IE 110 = one hundred and ten, 4 words)
I voted for 1.
Although I follow and appreciate all the 9 explanations, I think the above posts nicely explain why we are ALL RIGHT.
For me in particular I would be more inclined to accept 9 if the problem had been set out as 6÷2x(2+1) instead of 6÷2(2+1)
But because the 2 is adjacent to the parenthesis it looks like they are connected in a more intimate and therefore immediate way than are the 6 and 2.
As another post pointed out, 6(2+1)÷2 would be more obviously 9 than would 6÷2(2+1), because 2(2+1) appears to be (2*2) + (2*1)
In a democracy we might say that the answer with the most votes is the correct one, but we might be wrong... it is only the accepted one
Without the additional parenthesis to clear up the ambiguity it is as clear as saying "I helped my uncle jack off his horse" without adding the necessary capitals
And my guess at XplosiV's puzzle (after his clarification that he meant the smallest number) is... one half dozen