Sudoku strategies explained with graphics

Strategies


Overview Singles Naked Pairs Naked Triples Hidden Pairs Hidden Triples Naked Quads Hidden Quads Pointing Pair Pointing Triple Box Reduction X-Wing Finned X-Wing Sashimi Finned X-Wing Franken X-Wing Finned Mutant X-Wing Skyscraper Chute Remote Pairs Simple Coloring Y-Wing W-Wing Swordfish Finned Swordfish Sashimi Finned Swordfish Franken Swordfish Mutant Swordfish Finned Mutant Swordfish Sashimi Finned Mutant Swordfish Sue De Coq XYZ-Wing X-Cycle Bi-Value Universal Grave XY-Chain 3D Medusa Jellyfish Jellyfish Jellyfish Avoidable Rectangle Unique Rectangle Hidden Unique Rectangle WXYZ-Wing Firework Subset Exclusion Empty Rectangle Sue De Coq Extended SK Loop Exocet Almost Locked Sets Alternating Inference Chain Digit Forcing Chains Nishio Forcing Chains Cell Forcing Chains Unit Forcing Chains Almost Locked Sets Forcing Chain Death Blossom Pattern Overlay Bowman Bingo



Subset Exclusion


Let us define an "Almost Locked Set" ("ALS" in short) as a set of n Cells in the same region (Row, Column or Square) containing in total exactly (n+1) Candidates: eg a "Bi-Value" Cell or two "Bi-Value" Cells with a common Candidate.


illustration not available, sorry

The combinations of the Candidates of two cells can not duplicate any combination of the Candidates of the "ALS" they both entirely see.

Indeed, if such a combination were the solution for these two Cells, then the two corresponding Candidates would be eliminated from the "ALS", which would then only contain (n-1) Candidates in total for n Cells.

In the example if Candidate 6 were the solution in H3, then

  • Candidate 3 as solution in H2 would empty Cell H6 and leave only one candidate in ALS {H5, H6}
  • Candidate 7 as solution in H2 would leave only Candidates 2, 4 and 8 in ALS {G1, G2, G3, J2}
which is not possible.



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