I don't know which boy?

Is it correct to say:

I don't know which boy you meet.

For me which here makes sense but grammatically I think there is something wrong by using which to refer to the boy.

Solution 1:

In your example, which is not a relative pronoun, but a determiner, pre-modifying boy. As a determiner, it can be used with animate and inanimate nouns. The sentence is grammatical, but it’s hard to understand what it means out of context. It would be more likely to occur as ‘I don't know which boy you are meeting.’

Unlike the first sentence, the second one contains not one, but two, relative clauses, but it, too, is a most unusual sentence. Its most natural manifestation would be as ‘I don't know who the boy you are meeting is’.

The first relative clause is ‘who the boy. . . is’. The second is ‘you are meeting’. This second one omits the relative pronoun, but if you want to include it, you can. In that case it would be either that, who or whom. A relative clause can be introduced by that when, as here, it forms part of an integrated relative clause, also known as a defining relative clause or a restrictive relative clause. The choice between who and whom, in both relative clauses, depends on the formality of the context, with who being less formal, and probably more frequent, but both are found in Standard English. In relative clauses, which acts differently from when it is a determiner. In a relative clause, it can only refer to inanimate antecedents.

Solution 2:

The sentence is grammatical and there is nothing wrong with using which as a determiner (I don't know which boy you meet) and relative pronoun (That is the boy which she met) even when you are describing a person. However, bear in mind, the sentence "I don't know who the boy that you meet is." is slightly different from "I don't know which boy you meet." because when which is used, it is referring to something among a group of things:

There are many boys that you meet, which one is he?

[Updates] I'd suggest you to use the sentence "I don't know which boy you met" or "I don't know which boy you have met" if the meeting has already taken place.