Why is the answer 104? My brain tells me it’s 4?
50 + 50 = 100
100 − 0 = 100
100 + 2 = 102
102 + 2 = 104
If you just evaluate left-to-right, it’s 4.
But the mathematical convention is to perform operations by precedence, and multiplication has a higher precedence than addition.
So 25x0 is done first, which is 0, then 50+50+(0)+2+2= 104.
I’ve seen a lot of problems like this floating around, but IMO they are ridiculous. They’re designed to trip people up about the order of operations. But nobody would ever write an expression like that in real life.
Yeah, I very. vividly remember my math teacher telling me to do the equations in the (x) first and then do the rest.
Technology Review, the MIT Alumni magazine, has a yearly challenge where you are supposed to build numbers from 1 to 100 using only the digits in the year. It was a lot of fun in 2000! That’s where you wouls see it, or something like that.
Also if parentheses are very expensive, I suppose.
It’s easy if you ever wrote a grammar for a computer language or implemented a parser for one.
Yeah. I think the concept of order of operations is useful and students should learn the convention but at a practical level you would never write an expression like this.
Why not?
The OP does not specify where he saw or from where he adapted his expression, but I would totally write an expression of the form a+b-cd+e+f which is completely clear and unambiguous, and you should too. The ISO might suggest to avoid a/bc, but when such expressions are not confusing you may as well write them as well, along with \log x/\log y, and 2n!, etc.
BODMAS or PODMAS, depending on which side of the Atlantic you learned arithmetic. Also BIDMAS, POMDAS etc.
Brackets/Parentheses, Orders/Indices, Division, Multiplication, Addition, Subtraction.
I seem to get around one of these a week on FB. I stopped bothering a long time ago.
Get around one a week of what? Do you have a good example (I’m sure they exist), let’s say from a textbook, article, or preprint, of some arithmetical expression one cannot easily interpret? I am not convinced this turns out to be such a problem in practice, concerning notation that has been around for centuries. Not that the ISO does not make a good point when they say not to write stuff like a/b/c, I just don’t think there is a problem with, e.g., (2x)!(-\frac{1}{2})!/2^{2x} or x-x^3/3! + x^5/5!.
[quote]Why not?
The OP does not specify where he saw or from where he adapted his expression, but I would totally write an expression of the form a+b-cd+e+f which is completely clear and unambiguous, and you should too. [/quote]
But that isn’t quite the same as the expression in the OP which would be a+b-cxd+e+f. Removing the multiplication sign does make it clear that multiplication comes first and the rest is straightforward.
Do you have to use all numbers, and can you use numbers twice? Otherwise
0!
0! + 0!
0! + 0! + 0!
And so on
They pop up, usually as a picture with a caption suggesting that 80/90% of all viewers will be unable to solve it.
They are simply click bait, appealing to people who like to think that they are above average in maths.
The question does not test mathematics ability at all, just whether you can remember the order of operations, which is a completely arbitrary convention.
Arithmetic isn’t mathematics.
Two areas where I get annoyed or fumble.
There is an element of visual parsing that happens when you are used to a particular form. That can sometimes lead you astray. Most of us will recognise say a polynomial expression and cease paying attention to the exact symbols involved and quickly just look at the pattern of coefficients, and so on. This can trip one up. Most areas have similar gotchas. The most common Internet puzzle is the one of the form:
9 \div 3 (2+1)
We had a thread a while ago on it. Visual parsing usually gets one what is technically the wrong answer. There is a form everyone recognises, but it isn’t what we think.
Writing code for reasonably complicated expressions can become a mess. I always add redundant brackets and lay out the expression across lines with indentation to provide for a visual guidance on how terms are collected and related. My pet hate is any IDE that insists that it knows better, when it automatically reduces the expression, removing redundant brackets and filling the line, killing the formatting.
Very true, but it should still be the responsibility of whoever is writing figures to avoid “tripping one up”. That way nothing explodes 
I feel confident we all think it would immediately be sent back for revision, and therefore has no chance of producing a wrong answer!
I am not in charge of Internet weird arithmetic puzzles, but it would be better for the pop-up authors to stick to the usual 1+2+3+4+\cdots=\zeta(-1) and other things which may be actually interesting.
Some of the places I’ve seen this “problem,” it comes with the instruction not to use a calculator.
If you type 50+50-25x0+2+2 into a basic, four-function calculator, it will perform the operations left to right and give you a result of 4.
If you type it into a scientific calculator (or a calculator app in scientific mode), it will follow the rules about the order of operations and give you 104.
Google’s calculator will make it clear how it’s evaluating the expression by sticking in parentheses:
50 + 50 - (25 x 0) + 2 + 2
Yeah, I think the “expected” answer is 104 but I’ll stand up for anybody who says it’s 4.
The point of an order of operations is not to impose some arbitrary set of rules (it’s more of a convention anyway - there’s no ‘Council of Math’ to set or enforce such rules) but to bring clarity when there is ambiguity.
In this case, the expression is written to deliberately introduce ambiguity. That’s called “missing the point”.
I don’t look at that and see “Oh, the answer is…”, for any value of the answer. I look at that and see “That’s a poorly-written problem”. If there were some context clues like units, I might try to figure out what the problem-writer intended, but without any context at all, my brain just skips straight over it.
But that (what you are saying) in turn misses what is commonly the point of math problems. To introduce the appearance of ambiguity that demands an understanding of the rules to find clarity, usually by applying “some arbitrary set of rules,” which all mathematical expression is in the end. 2+2=4 only because some people arbitrarily decided that the associated quantities and operations should be represented by those signs/characters.