Never believe it when a student says their teacher didn't teach something in class since that is always their fall back excuse.  It seems they knew what "cardinality" of a set meant, so surely they learned something about set theory.

If I knew what sets, unions, and cardinalities were, I'm sure I would've understood and solved this question much younger than 9th grade. Somehow it sounds more intimidating when I think of it as a math exam question vs. as a puzzle. It's the kind of puzzle they put in recreational math books for middle schoolers. But it's the kind of math exam question you could get in undergrad. idk math is a great big thing to explore, how wonderful that kids and adults alike can partake!

I don't think I'd be able to solve this in ninth grade. We only got set theory much later, sadly.

OP's pal's workaround proves that he was well familiar with the subject of the problem (sets, unions, cardinality), even if he didn't know how to solve the general question.

There's no reason other than lack of instruction that a 9th grade student shouldn't be able to solve this. Sets are not a particularly complicated concept at this level. Reframed, this would be a fine medium or maybe hard puzzle for a professor layton game.

However, our math curriculum in the US is just kind of crap. If there is no instruction on the topic, if you don't know what a set is or what a union is, this is basically impossible as presented.

There are 150 elements in all of the sets, and each element is 'counted' ten times over.
Hence, the cardinality of S is 15.

Yeah, you can multiply 30 sets by 5 elements alright but you forgot to divide by 10

In Sweden in the '70s and '80s there was a widely used set of math textbooks for primary and lower secondary school called "Hej Matematik!" ("Hello Mathematics") that taught set theory. I did not experience this myself but according to Wikipedia set theory was somehow used to teach arithmetic to kids in these books. It generally doesn't seem to be viewed as a very successful experiment.

Im in 12th grade, learned a bit about sets in my stats class, had to think about it for a minute before I could find the answer. Here`s what I did: (before watching the video)
1. 30 sets of 5 elements = 150 elements in total (NOT EXCLUSIVE/UNIQUE)
2. Each element of S is contained in exactly 10 sets ==> each element is counted 10 times
3. Every single element in An must be in S (An being the Union from 1 to 30 of A)
4. Since each element is counted 10 times too much(a specific element a appears in exactly 10 set, for every a in A), An = 150/10 = 15,
5. n(An) = n(S) = 15

I have a request. Please make a video on Lebesgue measure. Its a topic not many people know, but I guarantee 99.99% will get the answer wrong

30 sets with 5 elements --> 30*5=150 elements.  Each element in S in 10 sets.  So 150/10=15 unique elements.

Did it the same way as the other kid in the post did. Finding a special case is often the easiest way to do it when given limited info.

In school, I was in GT math and took all my classes a year early. So 8th grade was geometry and 9th grade was precalculus. I'm a little fuzzy on what concepts were taught in what grade, but I was definitely doing intro to matrices in 9th grade, so intro to sets wouldn't feel too out of place.

Veryyy Similar to NCERT Exemplar Grade-11th Problem 29 (Objective), India.

I'm so dumb I way overcomplicated it:
Each element has a 1/3 chance of being in a given set
Each element has a 2/3 chance of NOT being in a given set
There are (S-1)(S-2)(S-3)(S-4)(S-5) /120 possible sets of 5 that don't contain a given element
There are (S)(S-1)(S-2)(S-3)(S-4)/120 sets in total
(S-1)(S-2)(S-3)(S-4)(S-5)
--------------------------------------- =2/3
(S)(S-1)(S-2)(S-3)(S-4)

This cancels to (S-5)/(S)=2/3
10/15=2/3 so S=15

Lol

Sadly, I have to agree with the assessment of US students.  I distinctly remember looking around the people I graduated with, and thinking "*these* people are going to be voting next year?"

In 4th or 5th grade, I got selected for a "gifted" program.  Looking back, I think I was not so much "gifted" as "interested".  I have always been interested in a great many things, and will cheerfully spend hours learning things that will never be of any use to me.  Most American students simply aren't interested in much at all.

My 9th graders could absolutely do this problem if they were being taught about sets. I have 9th grade twins in two different high schools right now (one wants to be a vet and is going to a school that offers special classes for that in addition to regular school). One is learning algebra and the other geometry. But this isn't any harder. Just different.

I solved it very quickly using the same method as in 8:20 which is how I would have explained it to them.

Yeah, if they actually know what the union operator and "cardinality of S" mean, then I kinda doubt that statement about it being "not at all related to  what was taught in class".  They arguably proved that they were taught enough in class that they theoretically should be able to figure out the correct answer, because arguably all you really need to know is the rules for sets and basic set operations, and what "cardinality" means (and be able to do some logical reasoning), to answer this.

I'm from Portugal, and I think I recall learning basic set theory around 9th grade. I'm 30 now, so it was a while ago, but I think that sounds correct.

On the students using calculators part,: I used to be sat next a guy in 10th or 11th grade, and he'd use his calculator for the most basic of things. Multiplying by zero, adding one, dividing a number by itself, you name it. One time I asked if he really didn't know what some number plus 1 was, and he said something along the lines of "of course I do, I just wanna make sure in case I don't make a stupid mistake." One time he was gonna do some plus zero and I just looked at him and he said "ok fine that's dumb", wrote the answer down, and then immediately typed it in the calculator,, saying "no, I gotta make sure!". One time I even caught him typing 1+1 into it...

Once Shawn became a motivational speaker so said to people when we work together we get more results like when a&b are squared separately we only get a2&b2 but when we square a+b we get a2 & b2 with extra 2ab😂😂😂