Finned Pointing Chains detect pointing patterns with a fin cell that forces a hidden single. A visual, human-friendly technique — spot the pointing pair, notice the fin, place the digit. No elimination needed.
Generalized contradiction testing. Assume a candidate is true, propagate through L1+L2 logic — if a contradiction emerges, that candidate is eliminated. The single most powerful technique in the pipeline.
Pick a bi-value cell. Branch on each candidate and run the full FPCE engine on both branches. Any elimination that appears in every branch is proven — a two-level proof by exhaustion.
The ultimate technique. Branch on each candidate in a cell, run the entire solver pipeline on each branch. If all but one lead to contradiction, the survivor is proven.
Pick a bivalue or trivalue cell. Branch on each candidate and propagate — if every branch forces the same conclusion, that conclusion is proven. Cleaner and faster than Nishio, with full contradiction tracing.
The wider sibling of Forcing Chains. Branch on cells with 3–4 candidates, propagate deeper through the constraint network. When all branches converge on the same elimination — it’s proven across the entire possibility space.
Tested against all 1,465 puzzles in the Top1465 benchmark — the hardest known set. Verified across 100 symmetry-shuffled variants per puzzle. Every placement proven by contradiction. Every elimination traceable.
“For each candidate it can only be ON or OFF — so if you try both then you are not guessing anymore, just being logical and thorough.”
— Andrew Stuart, creator of SudokuWiki.org