When Logic Fails: The Guess-and-Check Method
Sometimes pure deduction is not enough. Learn when and how to use trial-and-error effectively.
The Forbidden Technique?
Purists hate it. Speed solvers tolerate it. Computers rely on it. We're talking about Bifurcation, commonly known as Guess-and-Check.
The honest truth is that some "Diabolical" level puzzles are designed to require look-ahead so deep that it effectively becomes trial and error. Our engine rates these as Level 4+.
When to Guess
Never guess early. Guessing is a last resort. Only use it when:
- You have scanned every number, corner, and edge.
- You have checked all "diagonal 3" and "0" patterns.
- You have tried inside/outside coloring logic.
- You are completely stuck with no forced moves.
How to Guess Efficiently (Bifurcation)
Don't just randomly draw a line. Be surgical.
1. Pick a "Binary" Spot: Find an edge that has the most impact. Usually, an edge shared by two numbers (e.g., between a 2 and a 3) is a good candidate. It can only be a LINE or an X.
Here's the bifurcation process visualized:
Start: Pick the ? edge Branch A: Assume LINE
·───· · · ·───· · ·
│ 3 2 1 │ 3 ║ 2 1
· · ? · · · ·═══· ·
2 ║ 2
· · · · · · × · ·
Which way does ? go? Follow the chain...
Branch A continued: Branch B: Assume X
→ CONTRADICTION! (since A failed)
·───· · · ·───· · ·
│ 3 ║ 2 1 │ 3 × 2 1
· ·═══· · · · × · ·
║ 2 ← needs 2 but 2
· · × · × · · · · ·
has 3! Impossible! ? is × (proven!)
2. Assume "LINE": Lightly draw the line (or use a different color mentally). Follow the chain reaction. "If this is a line, that must be X, so that must be line..."
3. Look for Contradictions: Does your chain reaction lead to a dead end? A vertex with 3 lines? A number that can't be satisfied?
If YES (Contradiction): Great! Your assumption was wrong. The edge MUST be an X. Mark it permanently and continue solving.
4. The "No Contradiction" Case: If you follow the chain for 10 steps and everything looks fine... stop. Undo. Try assuming "X" instead. If that leads to a contradiction, then the edge MUST be a LINE.
The "Undo" Button is Your Safety Net
Modern digital implementations (like ours) have an Undo button. This makes bifurcation much safer.
Tip: Before guessing, memorize the state of the board or take a mental snapshot. "I am testing the edge between the 3 and the 1." If it fails, you can quickly revert.
The Golden Rule
If you have to guess more than 2 levels deep (guessing on a guess), you are probably missing a logical deduction. Back up and look for a simpler pattern you missed.