scrum master applying good judgement and logic

I let the people doing the work solve the problem instead of trying to force my will on them. 

Scrum Masters do not solve problems.  They make it possible for others to solve problems.

give an example when as a Scrum Master you applied good judgement and logic to solve a problem in an organisation

None are good; each example robbed the team of its creativity, and hence I failed.

Sounds like an interview question without a specific scenario! I see scenario based questions are common now, such as:

-How would you deal with a team lacking motivation?

-What would you do with a Product Owner directly assigning work or always asking for more work to be done in the middle of a Sprint that has nothing to do with the Sprint Goal?

-How would you deal with a reluctant team member or unhealthy conflict?

For a Scrum Master I think the good judgement and logic are the steps you took to coach, teach or facilitate and knowing what method is appropriate. Its always good to have some examples of how you are commercially aware too, stakeholder management is coming up a lot in interviews!