"Is there a" vs "is there any"?

Question

Which one of these is right?

Is there a way [...]?

Is there any way [...]?

May I use either? If yes, what's the difference?

Answer 1

The expression a way alludes to one particular way. The expression any way alludes to one of any number of possible ways.

As you mentioned in your astute comment, at the time of asking the question, there's really no difference. Yes, you can use either one of them – in this context.

Consider:

Is there a way to roll babookamitzes uphill, without breaking into a sweat?
Is there any way to roll babookamitzes uphill, without breaking into a sweat?

I would say that these questions have no difference in meaning. Why? Let's assume I know three ways to accomplish this task. No matter which question you asked me, my answer would be the same:

Yes, I know at least three ways to do that.

I would not be more or less inclined to mention only one method if you used a way instead of any way, or vice-versa.

In other contexts, though, the words a and any are not interchangeable. In fact, in some contexts, replacing one with the other would result in an ungrammatical statement:

I know a way we can get to Timbuktu from Constantinople. okay
I know any way we can get to Timbuktu from Constantinople. incorrect

Any time we try to plan a picnic, it rains. okay
A time we try to plan a picnic, it rains. incorrect

But, in the context of asking a question about solving a problem, either one is just fine:

Do you know a way we can get to Timbuktu from Constantinople?
Do you know any way we can get to Timbuktu from Constantinople?
_{(answer to both questions: Yes: we can fly, or take a train.)}

Answer 2

I have to partially disagree with extend J.R.'s answer here. They are correct that when asking the question               

Is there any/a way to...

it is often the case that the two words are interchangeable. However, this is only the case when there's a neutral tone to the question. For instance, the question       

Is there a way to draw a perfect circle?

works just as well as

Is there any way to draw a perfect circle?

But if the question has an implicit extra meaning, then this is no longer the case. For instance, after spending several hours trying to draw a perfect circle, one might yell

Is there any way to draw a perfect circle?

In which case any cannot simply be replaced with a, as it would remove the speaker's implicit suggestion that no such method appears to exist. Not to mention that emphasizing a comes off as an awkward speech pattern here. By shifting the emphasis, one could get the sentence

Is there a way to draw a perfect circle?

Which is very similar, but has, to my mind, a slightly different tone.

Similarly, if your neighbour is blasting music, one may ask

Is there any way you could turn down the music?

Which does not work as well with a, because any suggests an uncertainty. In this case this is done to make the phrase more polite. You are requesting that the volume be lowered, but allowing for the possibility that the volume has a good reason to be high.

In summary, I would say that using a usually expresses a lack of assumptions about the answer to the question, while using any can suggest that one doubts or is uncertain of the existence of a solution.    

Edit: If in doubt, I would favour always using any over a in a question like this, as I am at a loss for any context in which a could not reasonably be replaced with any.     

Answer 3

I think J.R. and Alexis are correct, although I would add that when asking a question in this manner "any" often adds a nuance that the speaker expects that the answer will be "no" or something negative.

For these examples:

• A: Is there a way to roll babookamitzes uphill, without breaking into a sweat?
• B: Is there any way to roll babookamitzes uphill, without breaking into a sweat?

"A" sounds neutral, however "B" has a more negative nuance implying that the speaker thinks that answer is no.

Answer 4

Both are correct!

Is there a way? - You are a bit specific about that way (though you don't know).
Is there any way? - You are talking about some way without any specification.