Great question. There is indeed a unique solution, but it's not intended for the player to use that information. (Which is why the rules don't mention that guarantee). I considered a couple of alternatives when writing this:
1. Don't have a single solution, but have any duplicate solutions be trivially transformable to the others. E.g. via the "this piece has two possible orientations, and neither will conflict with another piece".
2. Make having a single solution be part of the rules, and necessary for solving some of the puzzles.
3. Make sure the puzzle generator just never generates a place where the uniqueness of the solution can be used to short-circuit the solution.
4. Punt.
Idea number 1 is probably the best one, but the fear was that players would perceive that as "guessing". But looking at how people actually play the game, I think that fear might have been misplaced.
1. Don't have a single solution, but have any duplicate solutions be trivially transformable to the others. E.g. via the "this piece has two possible orientations, and neither will conflict with another piece".
2. Make having a single solution be part of the rules, and necessary for solving some of the puzzles.
3. Make sure the puzzle generator just never generates a place where the uniqueness of the solution can be used to short-circuit the solution.
4. Punt.
Idea number 1 is probably the best one, but the fear was that players would perceive that as "guessing". But looking at how people actually play the game, I think that fear might have been misplaced.