Tier 3
Exclusion logic
The last resort, and still not guessing — try a square, push the easy logic two steps, and rule it out when the board breaks.
Every puzzle here is solvable without guessing. But “without guessing” does not mean “without hypotheticals”: there is a real difference between trying a square and keeping it because nothing went wrong, which is guessing, and trying a square and rejecting it because something did, which is proof.
The method:
- Pick a square that still looks possible.
- Pretend the queen is there.
- Run only the cheap techniques — adjacency, completions, containment.
- If some row, column or colour ends up with nowhere to go, the square is impossible. Cross it off and forget the whole hypothetical.
- If nothing breaks, learn nothing. Undo and try elsewhere.
Step 5 is the discipline. A hypothesis that does not blow up tells you nothing at all, and treating it as encouragement is how people end up with an unsolvable board twenty moves later.
Keeping it honest
Two rules keep this from becoming trial and error:
- Depth limit. Two or three steps of cheap logic, no more. If you need ten, you are not proving anything, you are exploring.
- No partial credit. Either the hypothesis dies or it never happened. Nothing you noticed inside a failed line carries out of it except the one elimination.
Where it fits
Reach for it only when counting, containment and clumps have all gone quiet. On our boards that is rare — most puzzles that need this at all need it exactly once, to break one stubborn square, after which the rest falls out by region completion.