Yay, math!
There's no conclusive answer because of the bad syntax in "6÷2(1+2)".
This is the only answer I can agree with.
We do not know the answer because the equation is not written correctly.
It's not bad syntax, it's proper syntax. Redundant parenthesis are not proper. There is only one way to properly interpret the given computation, and adding any more parenthesis would either change the meaning, or be redundant.
Disagreed. Parenthesis would not be redundant. I think the problem lies with the fact that some people believe that you should work from left to right. But I disagree on that.
An equation should be solvable in any order.
x*y = xy
xy = yx (commutativity)
So, in the case: 6 / (2(1+2)) we are allowed to switch (2(1+2)) with this ((1+2)2). Its the same, right?
In the case (6 / 2)(1+2) we are allowed to switch (6 / 2)(1+2) with (1+2)(6 / 2). Its the same, right?
The parenthesis tell you what you may commute and what not.
Since 6 / 2(1+2) does not contain any parenthesis that prohibit me from commuting 2(1+2), I should be able to do so. 6 / (1+2)2
And, we can all see that if we do so, following the left-to-right method does no longer work.
So I would say, that by these rules, if you would follow Veeno's rules, you're just placing imaginary parenthesis to help you out. Thus they are not redundant.
There is also a proof using binary trees. I wont draw it out, but it concludes that you can not write binary tree that contains the equation 6 / 2(1+2). It will either be 6 / (2(1+2)) or (6 / 2)(1+2)
(If you are willing to except that any valid equation can be writtin in a binary tree form)
Now, I would like to mention a few things.
1) Is commuting even a word? I just hope you all get me.
2) This is the view of a first year Computer Science student. Its all based that on the rule "An equation should be solvable in any order." we learn.
3) I will now hide from the wrath of Veeno
*Goes of running into the dark night, hoping he will not be found*