I've got what should be a simple question. If a problem already exists, and there is a variation using the same highest handhold with the other hand, the same foothold, and goes to the same pocket and topout, is it a separate problem or just another solution?

So you're saying the only difference is that you use your left hand on a hold instead of your right? That sounds like the same problem. I wouldn't even call it a variation, it's just different beta.

That's pretty much what I thought.

It depends on what the tape says at the bottom.

Its just different beta. Unless youre in lincoln woods or central park, then its a different name and a different rating

It depends on how bored the climbers in the area are.