Deduce, don’t guess

Every puzzle here has a unique solution, and logic alone can reach it. But sometimes the next step is hard to see, and it is tempting to guess.

There is an honest way to do it. Pick a cell with two options. Suppose one. Make only moves that are forced from there. If you reach a contradiction, the supposition was false, and the other option is proved. That is proof by contradiction, and solvers call it bifurcation.

The dishonest way is to guess and carry on as if the guess were true. If it was wrong, you find out twenty moves later with no idea where it went wrong.

One: pick a cell with exactly two candidates. Two: suppose one of them. Three: make only forced moves, singles and nothing else. Four: if something breaks, the other candidate is proved.

Five: if nothing breaks after a few moves, undo all of it. A supposition that holds up for a while proves nothing. It might break later, or the other option might work too.

If a supposition leads all the way to a finished grid, and the puzzle is known to have one solution, then you have found it. Without that promise, a finished grid only shows one answer, not the answer.