This isn't always true. Some interviews are really about solving the problems as fast as possible. And lots of interviewers are looking for exactly the answer they have on hand, and will think you're doing it wrong if you come up with a different, but equally valid (or better!) solution.
I was asked to sketch the proof for the irrationality of sqrt(2) in a quant programming interview. I kind of froze, and explained that though I had learned it, I could not recall.
He prompted me with "Well, what does it mean to be irrational?", and with that little hint I did the rest. Though ultimately I did not end up working there, it was very satisfying to have answered it.
Well, in one case (me), all the information the interviewer had was "this guy happens to know how to implement a quick sort by heart. K.".
In the other case (my friend), he got "this guy is able to understand and implement an algo he never saw before in a reasonable time", which is much more impressive
> We now show that the equation (1) p^2=2 is not satisfied by any rational p. If there were such a p, we could write p=m/n where m and n are integers that are not both even. Let us assume this is done. Then (1) implies (2) m^2=2n^2. This shows m^2 is even. Hence m is even (if m were odd, m^2 would be odd), and so m^2 is divisible by 4. It follows that the right side of (2) is divisible by 4, so that n^2 is even, which implies that n is even. > The assumption that (1) holds leads to the conclusion that both m and n are even, contrary to our choice of m and n. Hence (1) is impossible for rational p.
Assume sqrt(2) is rational and has the reduced form (x/y). Thus we are assuming that x and y are integers and that gcd(x,y) is 1. You square it and get x^2/y^2 which are somehow simultaneously coprime integers and also reducible to 2/1...
Huge asterisk that as long as you arrive to the correct solution with minimal help. I've had plenty of algo/ds interviews and it seems like needing help to see the trick in the question pretty much means you're out.
In many of the places that do claim this, even if you solve the problem "correctly" you still get more brownie points than someone who got a less efficient answer or didn't get an answer. Meaning that they /do/ actually care. I do get that some places are smarter with regards to this than others but it's depressingly common in my experience. "You didn't get the O(n) solution that has weird edge cases and was published as a paper in the 70s? Too bad, because some other person did, because they remember the solution from some programming interview book!"
At my last company, we would sit a candidate down at a pairing station. We'd offer them about 5 problems to choose from, and together we'd pair program on the problem for 2 hours. Using the internet, the IDE, anything they want was totally fair game. No system is perfect, but this was by far the best one I've ever experienced.
They were probably looking for the answer of, "Lets talk through it and figure out a better answer". Coders are often under a mistaken impression that interviewers care about your answer. They don't. They care about how you approach it, how you think through it, what you do when challenged, etc.
So from their perspective, they asked you to try harder on a problem, and you just said, "No." And they dropped you for it.
FWIW, I had similar questions in some interviews where we hashed through similar problems, and together collaborated down to a "No" answer... but we spent 15 minutes exploring the problem and seeing how well a couple coders can work through it before saying no. And I got the offer despite an otherwise rusty performance.