Proven Sudoku
Techniques / Exotic and rank-zero
Rank Theory
Also called Rank logic, Set cover rank, Rank 0 logic.
New to this shorthand? How to read a sudoku grid explains r4c7, houses, candidates and the rest.
What it means
A way to count a pattern. Count how many groups need a number. Count how many spots they have. When the two are equal, nothing is spare, and the rest has to go.
The exact rule, for stronger players
The rule, stated exactly: Given a set of base sets and cover sets over truths in the grid, rank is covers minus bases. At rank zero every truth is used exactly once, so any candidate not in a base but in a cover is false. Positive rank weakens the conclusion proportionally.
What it removes: At rank zero, eliminate cover candidates outside the bases. At higher rank, conclusions are conditional.
Why it works: Each base set contributes exactly one truth. If the covers can absorb no more than the bases supply, they are saturated and nothing else fits.
Worked examples
None yet. This pattern does not turn up in our daily boards, so there is no real example to show. We would rather wait than draw a fake one.
Learn these first
- Complex Fish (rank framework)The fish idea, but boxes are allowed to join the rows and columns.
Related exotic and rank-zero
- Senior ExocetA bigger version of the Exocet pattern, with more squares acting as the target.
- SK LoopA ring of almost complete sets passing through the corners of a band and a stack.
- Table-Driven MethodsWork out ahead of time what follows from each single guess, and store it in a table.
- Broken WingA ring of squares where one number would have nowhere to go if the ring were perfect.
- Domino LoopA ring of pairs that lean on each other all the way round, like falling dominoes.
How often does it come up?
Our rough estimate: this is the theory page that makes Tier 10 comprehensible rather than a list of unrelated exotica.