Techniques / Exotic and rank-zero

Exotic patterns: exocets, rank zero logic and MSLS

Whole-grid structures for the puzzles nothing else touches.

13 techniques in this family, introduced at tier 10. How to read a sudoku grid explains the notation used below.

What these have in common

These are not local shapes. Each one says something about a big part of the grid at once. Most are best read through rank, which counts how much slack a layout has left.

Why the logic holds

Fish work by matching base sets against cover sets. Rank is just the count of cover sets minus base sets. When that comes to zero, every truth in the base sets is used up exactly, with none spare. Any candidate that sits in a cover set but not a base set is then dead, because there is no room left for it. A surprising number of the hardest known shapes turn out to be that one idea.

When to reach for it

On the small number of published puzzles that defeat everything else, and in practice with software assistance.

How the members differ

Multi-Sector Locked Sets and the SK and Domino loops are rank zero shapes built over linked houses. Exocets take a base pair of cells and two target cells, and show the base digits must land in the targets. The Junior, Senior and Double forms differ in how far the backing structure reaches. Fireworks and Broken Wing are their own shapes with their own arguments. Gurth's Symmetrical Placement is odd one out. It uses a symmetry in how the puzzle was built, not anything in the rules, so it only works on puzzles built that way. Pattern Overlay and table driven methods are plain search in a technique's clothing.

The mistake to avoid

Treating any of this as a skill to pick up. It is a body of work to read. Knowing rank zero exists is worth it for one reason: it shows why several shapes that look unrelated are the same result.

Every technique in this family

• 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.
• Double ExocetTwo of those launcher patterns sharing the same numbers.
• FireworksA number is trapped so that it can only sit in one row, one column, or the square where they cross.
• Gurth's Symmetrical PlacementSome puzzles are built with a mirror pattern.
• Homogeneous ChainsA chain where every link is the same kind.
• Junior ExocetTwo squares act as a launcher and two more as the target.
• Multi-Sector Locked SetsCount several rows, columns and boxes at once.
• Pattern Overlay MethodEvery digit has to land in one of a fixed set of shapes across the grid.
• Rank TheoryA way to count a pattern.
• 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.