I really dislike the idea of open-ended, multiple-solution puzzles. At first, they seem like a cool idea. But it's a kind of "on paper" thing.
More solutions means the puzzle is easier, and it's more logical to just try things rather than think about them, because it's more likely that you can just stumble on one of the answers. Take, for instance, Scribblenauts. Its puzzles aren't really puzzles, because you have such a wide variety of solutions that any challenge comes from the game not doing what you told it to do.