One solution: what it means

A setter is the person who makes a puzzle. The first rule of setting is that the puzzle has a unique solution: exactly one way to fill the grid that follows every rule.

Why one? Because the solver reasons from the rules and the givens. If two answers fit, then at some point both are still possible, and no reasoning can choose between them. The solver has to guess, and a guess isn’t logic.

So every puzzle on this site has exactly one solution, and the same goes for anything we feature. This lesson shows what a second solution looks like, and how one more given removes it.

In the language of the logic lessons, “this puzzle has exactly one solution” says two things. There is a grid that follows every rule. And any grid that follows every rule is that grid. It is exactly one applied to whole answers.

The first half is easy to check: show the answer. The second half is the hard part, because it is about every possible grid. That is why setters use a computer to count solutions, which the testing lesson covers.

Taking a given away can make a puzzle harder, or it can break it. Once a second answer appears, the puzzle is not hard, it is unfair. Setters remove givens one at a time and test after each one.