I’m sure you’ve seen them on social media. Math problems that are trivial but are labeled as if they’re brain-busting conundrums. They often say things like “Only 1% of the people will get this right!” or perhaps “It takes a genius level IQ to solve this!”. These claims are, of course, lies. Like the germs on the fixtures of a public restroom, these problems do not exist to challenge your intellect but simply to spread.
As such, the most successful problems are not ones that are difficult, but ones that have ambiguity. Because ambiguity leads to arguments and nothing is more viral than an argument.
I have a low opinion of these sorts of things. Aside from being deliberately designed to start fights, they’re often low-quality images in a terrible font with a poorly expressed problem. I’ve seen a few which were actually wrong. Maybe they showed an incorrect answer. Maybe they were improperly expressed or labeled. Or maybe they suffered from bad grammar and punctuation. So when I glance at one of these and I disagree with the proffered conclusion, I usually assume it’s a garbage attempt at a meme rather than questioning my assumptions.
However, I ran into one over the weekend that was actually kind of clever. As obnoxious trollface problems go, this one was pretty good. It goes thus:
This is an exemplar of the form. Impact font? Check. Shitty quality and Jpeg artifacting? Check. Entices you to pay attention by questioning your mental prowess? Check. Shitty watermark from an off-brand image hosting site? Check.
A lot of these problems exploit the fact that a large segment of the general public doesn’t remember the order of operations from middle school. The naive thing to do is to work left to right. 230 minus 220 is 10, and 10 times ½ is 5. However, this is not correct.
When you’re following the proper order of operations, you calculate things in this order:
- Exponents and roots.
- Multiplication and division.
- Addition and subtraction.
Following these rules would have you multiply 220 by ½ to get 110, then subtract 110 from 230 to get 120.
So your typical art majorI’m sure many art majors are good at math. But sometimes stereotypes are useful. will get 5, your math major will get 120, and the problem itself states that the answer is 5! So now you’re going to have an argument in the comments where the math majors try to explain the order of operations to the art majors while a third, smaller group of provocateur math majors insist the art majors are “right” while snickering.
What you should know is that this problem is, first and foremost, a trollface. Secondly it’s a punctuation problem. Thirdly it’s a math problem.
You can clear up the whole thing by re-wording the conclusion to say something like, “The answer is (5!), but most people won’t believe it!”
See, in mathematics, the exclamation mark is an operator. It means factorial. If you’ve forgotten, n! means you multiply all positive integers less than or equal to n. So 5! would be:
Thus 5! = 120. And now you can see the problem. 120 is the correct answer. Thus 5! is also correct. But the naive answer of 5 is not correct. The conclusion is written so that 5 is at the end of the sentence and the sentence ends in an exclamation mark, so you’re likely to see the mark as emphasis, not factorial.
So if you’re used to seeing people mess up their order of operations problems then that’s what this appears to be.
There’s a bit of strangeness in the other parts of the problem as well. 220 × ½ looks odd to me. It’s totally correct, but typically if you’re trying to divide something in half you’ll either multiply by 0.5 or divide by two. You’re allowed to multiply by ½ if you like (and indeed, that’s what 0.5 is) but it looks unusual to my eyes. When I started to suspect this problem was engaging in a trick, I zeroed in on this bit looking for shenanigans.
The other giveaway that this is a troll problem is the fact that it gives away the “answer”. Most of these don’t, and leave you to work it out for yourself. But here the problem tells you the answer (in an ambiguous way) and then leaves you to argue about it in the comments.
Well played, internet.
EDIT: If you’re curious about the origin, the author stopped by with the goods. Here is the Reddit thread where the trick of punctuation vs. factorials was devised. And here is a blog post where someone else turned it into a troll question by having the problem work out to 5 if you botch the order of operations, thus setting the stage for chaos.
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