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While there are already many good answers, there's one option which I haven't seen mentioned (if I just missed it, sorry about that): Your hero may discover that the solution to the problem wasn't...
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#4: Attribution notice removed
Source: https://writers.stackexchange.com/a/39476 License name: CC BY-SA 3.0 License URL: https://creativecommons.org/licenses/by-sa/3.0/
#3: Attribution notice added
Source: https://writers.stackexchange.com/a/39476 License name: CC BY-SA 3.0 License URL: https://creativecommons.org/licenses/by-sa/3.0/
#2: Initial revision
While there are already many good answers, there's one option which I haven't seen mentioned (if I just missed it, sorry about that): Your hero may discover that the solution to the problem wasn't actually as good as thought. And now he has to fix it. For example, say the world had been held hostage by a powerful, evil wizard. Your hero finally managed to defeat the wizard by essentially disabling his magic. Great, problem solved, world saved. Well, except that in the next book, it turns out that there are side effects of this anti-magic. And the side effects turn out to be quite damaging in themselves. So now the hero has to actually re-enable magic, but in a way that the evil wizard does not regain his power.