Who run(s) the world?

Which of the following is correct? 

(1) Who runs the world? Girls!
(2) Who run the world? Girls! 

If your judgements match mine, you picked (1). But if you think about it, that's really weird. And it seems like at least some people find both of them OK. The two options are illustrated in these images that I collected within a day or so of each other without even looking for them: 

Who run the world? Girls

Who runs the world? [Image of a woman with a toddler, both raising their hands]

If they were statements, not questions, there wouldn't be a choice. (4) is ungrammatical in standard English and most of its varieties:

(3) Girls run the world
(4) *Girls runs the world

The reason (4) is ungrammatical (that's what the asterisk means) is because it has a plural subject (girls) and singular agreement on the verb (runs, rather than run).

To go back to our original examples, who doesn't have any information about whether it refers to a singular or a plural subject. It could be either, and (5), with a singular referent for who, is just as good as (1), where the referent is the plural girls.

(5) Who runs the world? Mark Zuckerberg. 

So that explains why it can cause either singular or plural agreement to appear on the verb.

And although I find it more natural with singular agreement, you can easily nudge it towards the plural agreement if there's a clear expectation that the answer is plural, such as if you know that the answer is either boys or girls, and you've forgotten which.

(6) Remind me, who did you say run the world? 

And that just leaves us with one mop-up, which is to say that the default if you don't have any information about number is to use the singular. That fits with the general principle that singular is the unmarked form: languages usually have some way of marking things as plural, not singular, just like English using -s for plurals and nothing for singular nouns (girl vs girls).