I think there'll be all manner of constraint and constraint-logic programming approaches that'd be amenable. I wish I had a great answer for you as "the best".

IMO, these "zebra puzzle"/"einstein puzzle" style problems are like a "hello world" for many related techniques. What's more, there are many languages that combine several of these techniques together so that you can easily pick and choose where appropriate.

If you were just wanting to compare against another related style, answer-set programming is one thing that comes to mind.