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Two solutions to the same problem have occurred to me within a few days. I tried to add the alternative solution, but the system suggested to edit my previous one. Should I add a new answer or edit a previous one in cases like this?

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This happens occasionally, and the results have also been varied. In some cases, users provide multiple solutions in a single answer (example). In other instances, users may provide multiple answers, each of which provide a distinct solution approach (example query). The former scenario is more the norm in my opinion.

The original question may request each answer to identify a separate instance/solution (example). However, if there's no such requirement set out, it depends on the answerer.

The system allows it, even though it provides a prompt when attempting to do so, so make sure it's not an addition to an existing answer and/or that it can be a "stand-alone, distinct and valid response".

Ultimately the community has a say in whatever choice is made based on their voting behaviour. That is, if it's considered more of an edit to an existing answer rather than a separate answer, I'm sure community members will raise the question in comments (perhaps chat), or via their voting.

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