"May I please have one of those biscuits?" asked Alice rather timedly, rather taken aback by the sight of her present company.

"A biscuit?? Oh, I don't know. Those are the March Hare's special un-birthday biscuits, don't you know. Can she have a biscuit, March ?" asked the Hatter.

"A biscuit?? One of mine? Hurmph. Ok, I'm thinking of an integer from one to three (inclusive). If you get it, you can have a biscuit. If not, I'm afraid you'll just have to leave" said the March Hare, leaning back.

"Oh goodness, I don't know" said Alice worriedly. "Couldn't I just get a hint?"

"Oh, all right..." the March Hare sighed. "You get to ask me one yes-or-no question, that's all"

Alice thought for a moment, then smiled, knowing exactly what to ask.

What question should Alice ask?

She could ask, "Is it prime," but if he says yes, 3 and 2 are possibilities (seeing as how 1 is neither a prime nor composite number).  If she asks, "Is it even/odd," she is risking the possibility of getting the choice of 3 or 1, which doesn't give her a definite answer.  She can't ask if it is a certain number, because that leaves the other two numbers open if she guesses the wrong number.  Out of these eliminated solutions, there are none other that I can think of, so I am concluding that the following is impossible.