There is more than one solution to every problem, but there is never a perfect solution, so don't waste your time looking for it. Find the best solution you can find in an appropriate amount of time, and implement it without hesitation.
When more than one person is affected by the problem, the most perfect solution possible is the one that everyone involved can accept (it is up to each person involved to speak up for themselves, it's not your responsibility). Anyone involved who refuses to even consider any solution other than the one they put forward should be immediately ejected from the game and thanked for playing.
Always come up with two solutions, Plan A and Plan B - to be used when Plan A fails. Plan B is never as good a solution as Plan A is, but it must be foolproof because there is no Plan C.