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I borrowed this story from my library around 30 years ago, so not much detail, but I remember it always intrigued me and I've always wanted to read it again.
I know there was at least one human left, a man I think, and there was something to do with machines/robots printing out answers; the last answer being quite devastating with no hope left for the man.
Could this be "The Last Question" by Asimov?
The last question was asked for the first time, half in jest, on May 21, 2061, at a time when humanity first stepped into the light. The question came about as a result of a five dollar bet over highballs, and it happened this way ...
"The Last Question" (ISFDbisfdb, Wikipedia) by Isaac Asimov.
The consciousness of AC encompassed all of what had been a Universe and brooded over what was now Chaos. Step by step, it must be done.
And AC said, "LET THERE BE LIGHT!"
And there was light--
Asimov has said multiple times that when someone can't remember the name of a story of his, the story is almost always The Last Question.
This has reached the point where I recently received a long-distance phone call from a desperate man who began, ‘Dr. Asimov, there’s a story I think you wrote, whose title I can’t remember–’ at which point I interrupted to tell him it was ‘The Last Question’ and when I described the plot it proved to be indeed the story he was after. I left him convinced I could read minds at a distance of a thousand miles.
Long shot, but perhaps PKD's "A Maze of Death" ? It features not a single man, but a very small group of people; machines (albeit mistaken for organisms for most of the story) called "tenches" that replicate things, but in the end return answers to questions given to them on a paper, and characters that get more and more despondent in the course of the story. Plus it was written in 1970, so you could have very well read it 30 years ago.
Since you have sparse details, it is possible that you're referring to "The Sixth Sally, or How Trurl and Klapaucius Created a Demon of the Second Kind to Defeat the Pirate Pugg", one of the tales in The Cyberiad by Stanislaw Lem. There, to escape a pirate, Trurl and Klapaucius create a "Demon of the Second Kind" (a reference to Maxwell's Demon) that essentially can separate fact from fiction from an infinite monkeys typewriter. The pirate is left trapped in the flood of truthful, but useless, information, always seeking that one gem of knowledge.
Where it doesn't match is that there is no "last answer" in sight, and that the characters are extremely human robots, not humans themselves.
The short story "The Nine Billion Names of God" by Arthur C. Clarke is about a man who goes on an expedition to Tibet, I think, and in a temple, they have a machine that is printing out the answer to all the possible names of God. They are excited because they think that the answer is almost complete.
The story ends with the man realizing that the answer is complete and at the same time, he looks up at the night sky and sees that 'all the stars were going out' as if the answer, in its completed form was destroying the universe.
Not sure if that's the one that you were looking for, but it fits the criteria I think. Good luck! :)
