The what-if method: choose an undecided edge, assume it’s a line (or a ✕), and apply only direct deductions. If you reach a broken rule, the assumption was false, so the opposite is proven. Undo the trial and record the result. Every Hard puzzle on this site can be solved with chains like this, each just a few steps long.
Guessing vs. proving
A guess is a move you keep without justification. A what-if is a temporary move you use to discover a contradiction. You only ever keep the conclusion — “this edge can’t be a line” — which is as certain as any pattern. Good solvers do this in their heads; you can also do it on the board and press Undo.
The method, step by step
- Exhaust the direct techniques first — black pearls, white pearls and loop logic.
- Pick a high-leverage edge: one with exactly two possibilities that touch a pearl or a loose end. The more constrained the area, the shorter the chain.
- Assume one option and follow only forced consequences.
- Look for a contradiction: a dead end, a branch, a black pearl going straight or with a short arm, a white pearl with no turn, a pearl that can’t be reached, or a premature loop.
- If you find one, the opposite option is proven. If you don’t within a few steps, undo and try another edge — don’t keep the trial.
Worked example
This position comes from the 6×6 puzzle in our worked example. The black pearl in the middle row is entered from the right; must it turn up or down?
So the black pearl turns down. And the same chain shows the top-left segment can’t drop down at all, so the two top segments join.
Both-ways deductions
Sometimes neither option of an edge leads to a contradiction — but both lead to the same consequence elsewhere. If “line here” forces edge X, and “✕ here” also forces edge X, then X is true regardless. Strong solvers use this to make progress when a contradiction is out of reach.
How to choose what to test
- Black pearls with two options left. Each option fixes two edges at once, so consequences come quickly.
- Loose ends near each other. Premature-loop contradictions appear fast.
- Narrow corridors near the edge. Dead ends cascade.
- Regions with few entrances, where a parity contradiction is likely.
Common pitfalls
- Long chains. If you’re more than six or seven steps in with no contradiction, stop. You’ve probably chosen a weak edge.
- Forgetting to undo. Mixing trial lines with proven lines is how errors creep in. On the board, use Undo until the trial is gone.
- Accepting a non-contradiction as proof. “It worked out so far” proves nothing. Only a broken rule proves the opposite.
Practice ladder
- 6×6 Hard — chains of two or three steps.
- 8×8 Hard — several what-ifs per puzzle.
- Weekly Masyu (15×15 Hard) — the real test.