Bilocation
When a digit has exactly two candidate cells in a unit. The underlying configuration that strong links, X-wings, and chain techniques all reach for as their starting shape.
Bilocation is the situation in which a digit has exactly two candidate cells within a unit. It's the building block underneath most intermediate and advanced techniques — a hidden single in waiting that hasn't yet been forced.
When a unit has bilocation on a digit, the digit must occupy one of the two cells, but you don't know which yet. That's already a strong link, and from the strong link a long catalogue of follow-on techniques becomes available. X-wings are coordinated bilocations across two rows; swordfish, three rows; chain techniques two-colour the bilocation graph for a digit and look for contradictions.
Why it has its own name
Bilocation gets a separate term because it's slightly distinct from "strong link" in scope. A strong link is the relationship; bilocation is the configuration that creates the relationship. Two cells form a strong link on digit 5 when 5 has exactly two candidate cells in their shared unit — and that "exactly two" is the bilocation. Talking about "the bilocation in box 3 on 5" is more compact than "the strong link in box 3 between (4, 7) and (5, 8) on 5." Reference works use both terms; chain literature leans on "bilocation" when describing graph structures, "strong link" when describing chain steps.
A closely related cousin
The two-candidate version of bilocation — a cell with exactly two candidates rather than a digit with exactly two candidate cells — is sometimes called a bivalue cell. Bivalue cells are what XY-chains and Almost Locked Sets are built from. They're the dual of bilocation: bilocation is "two cells, one digit"; bivalue is "one cell, two digits."
See also
- Strong link— A relationship between two cells in a unit where a digit must occupy exactly one of them — the basic primitive that hidden singles, X-wings, and chain reasoning all rest on.
- Weak link— A relationship between two cells where at most one can hold the digit. Looser than a strong link — both might be other digits — and the steady half of every chain technique.
- Candidate— A digit (1–9) a cell could still legally hold — one not yet ruled out by anything in its row, column, or 3×3 box. Every empty cell has between one and nine.
- X-wing— When a digit's only two cells across two rows form a rectangle in two columns — eliminating that digit from the rest of those columns. Or the same shape rotated 90°.
- Hidden single— A digit with only one possible cell within a unit (row, column, or 3×3 box) — even if that cell could legally hold other digits. The unit-first sibling of the naked single.
Read more
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