Confused about "Mate in n" puzzles

Hello there. I just started playing chess weeks ago, and I especially love those "mate in n" puzzles. But I am a bit confused about the definition of "mate in n."

For example, if I didn't take it wrong, the "mate in 2" means (1) I move, (2) the opposite response, and (3)then I checkmate.

But, if there are multiple optional moves I could choose in step (1), multiple optional responses of the opposite in step (2), and multiple possible endgames in (3), could I say it's a "mate in 2" as long as there is one endgame which is checkmate? Namely, one route is sufficient.

Or, rather, although there are multiple optional moves I could choose and multiple optional responses accordingly, I have to make sure that all these resulted endgames are checkmate? Namely, all routes are necessarily heading to checkmate.

I hope my poor English conveys the idea, and I would be appreciated for the friendly replies.

If There Is Written Make In 2 You Have to find only mate in 2 and they write mate in 2 because Mate In One isn't possible and if you find mate in 3 then find only mate in 2 (tricy question hard to understand)

Mate in N means that you have a position where the opponent can do nothing to prevent mate within N number of turns...provided that you also play the correct moves yourself. So your opponent's moves would essentially be forced, either by the king having a limited set of escape squares or a limit to how many of his pieces can legally move.

To give a really simplistic example, with white to go first, this is mate in 2. White of course has choices, with two rooks and a king to move and plenty of different squares to move to...but the fact is that if white chooses correctly then black cannot prevent mate in two moves.

When black moves his king, he also has choices of two squares, but the choice black makes is irrelevant.

So any mate in N opportunity can cease to be a mate opportunity if the attacker plays the wrong move. If the defender has a choice of moves, one of which breaks the mating opportunity then it ins't actually a mate in N puzzle at all.

So you need to find the moves that give your opponent no opportunity whatsoever to save themselves...

 Hey guys. I got it. It seems it's only necessary to find the route to mate,

For example, in this "mate in 2" puzzle I did just now:

white to move, 1. Nf6, .... Black may respond as 1. ..., Qxf6, then 2. Qxf8#. Or black may respond as 1. ..., Rg8, then 2. Qxh7#. 

Black is not forced to respond in either way (e.g., 1. ... Qa7). But if Black did respond as mentioned above, White's following right mate will lead to checkmate.

So doing the "mate in n" puzzle is to find the one or several routes heading to checkmate among all possible ones, not making all possible routes heading to checkmate...

Anyway, thanks for the replies!

If Black plays Qa7 (or anything else), 2. Qxh7 is checkmate.

I think you got your conclusion wrong (but I am not sure I understand you perfectly).

No, if it's "mate in 2", then there's no way for the opponent to avoid mate in 2. At all. That's the whole point.