reductio ad absurdum
I have found that some of the more difficult problems can be solved by a guessing of sorts.
1) Use clues provided to solve as much of the puzzle as possible.
2) Make a guess.
3) Complete the puzzle using what you can deduce from your assumption.
4) If you run into a contradiction (i.e. Sarah owns Bermuda and Key West) then you know that you have guessed incorrectly. Go back and resume the puzzle from the point where you guessed - this time making the opposite choice.
5) If you do not find a contradiction then you guessed correctly.
The key here - like what the other responses have indicated - is that there is enough information in the clues. Getting this information just requires more creative methods.