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As long as it takes to either

  - solve it, or

  - to realise that it's insoluble, or

  - to realise that the cost of finding a solution cannot justify the expected value of a solution.
I dont last longer than 3 months.

The first month or so is the "novelty seeking" high, usually exploring/learning something new and designing/building something basic with it. Second month involves getting feedback from people and continuing the build process. Third month involves working on the feedback and fixing bugs. This is usually where things start getting boring and I try to hand it off to whoever is most interested in the problem.

This style of functioning suits my personality type which is more neurotic than disciplined. And some probs require people who arent exploring the search space in methodical disciplined fashion but who jump around randomly.

This took a while to communicate properly to people esp bosses, who want you on the problem till the end if you show signs of progress.

What helped me was to get people to understand the Explore-Exploit Tradeoff and how different skills are required at different phases of the problem solving process.