In case (b), 1307 is as close to 1337 as are the example numbers 4337, 1037, and 1334 (among others). The found number could be closer to 1337 if it were instead 1347 or 1327 (among others).

This is the case I meant to (at least one that would be very close to what someone would use in real life). The point is to choose your own criteria for the example situation to determine whether that person is a real magician.

This can't be. If nothing else, the one group uses their left hand and the other uses their right. You need an "except" or "other than" clause.

I know, but in real life, left-handers can be a subject of stereotyping and discrimination. So I wanted to omit factors like those, like everyone does in such questions. I could have said that some have gene A and others have gene B and only you can identify people and nobody else cares about it, because it has no effect on anything, but handedness seemed more intuitive to me, for this already quite abstract question.

Did it just happen to turn out that we found ten, so we can proceed, and if we didn't find ten we'd skip this problem - or does this problem solely use classes that have ten and throw out other classes?

The problem only uses classes that have ten or more right-handers. I have edited this in the description.

In the entire class? Because that's not clear.

I have clarified that. I don't know why did I include this item, because it sort of duplicates a).

Went around shaking hands until locating a left-handed person, or grabbed the first person you saw and they were left-handed?

I have edited it to "randomly picked a left-handed person, out of all the left-handers who were there".

What, really? These are both heavily correlated with a third thing but not at all with each other? Are there real phenomena that act like that? It is unlikely to have good grades and a low score on either one, but they're not correlated?

Why not? The original was with IQ and concentration, but someone took it literally, so I decided to rename it. As far as I know, they + conscientiousness are all correlated with academic success, but not correlated with each other. Also, intelligence and social abilities are both correlated with social success.

I'm just nitpicking here, but this made me wonder if a won $35 would be taxed where the $10 wouldn't.

What do you mean? There are no taxes in either case.

This is bad wording if this is supposed to be an expected value question. The most money possible is just $35; you don't even have to work out the expected value. If you take the ten dollars you are not getting as much as you could possibly have gotten.

I think it's fine this way and I can't think of another way to word it. English isn't my first language.