Intermediate

Where easy puzzles end and the harder ones begin. X-wing, Y-wing, swordfish, and the structural concepts that chain reasoning depends on — strong links, weak links, bilocation.

14 entries

  • 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.

    Rules & terminology
  • Cross-reference

    Kakuro deduction at the intersection of two runs. The cell shared between a row run and a column run must hold a digit valid in both — usually pinning the cell directly.

    Techniques
  • Cross-unit 45 rule

    The 45 rule applied across two or more units that a cage spans. Sums and the cells that cross unit boundaries balance via the same 45-each-unit constraint.

    Techniques
  • Forced cell (kakuro)

    A kakuro placement where cross-reference and run constraints together pin a single cell to a single digit. The kakuro equivalent of a hidden single.

    Techniques
  • Innies and outies

    In Killer Sudoku, deducing a cell's digit by applying the 45 rule to a unit whose cages partly overlap with — or partly spill out of — that unit.

    Techniques
  • Kakuro pair

    Two cells in a kakuro run sharing the same two-digit possible set. The two digits are confined to those two cells, eliminating them from every other cell of the run.

    Techniques
  • Kakuro triple

    Three cells in a kakuro run sharing the same three-digit possible set — the kakuro analogue of the naked triple. Eliminates those digits from the rest of the run.

    Techniques
  • Partial cage combinations

    Killer-Sudoku reasoning where partial information about a cage's digits — eliminations, placements, or external constraints — narrows the cage's combinations to a smaller set.

    Techniques
  • 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.

    Rules & terminology
  • Swordfish

    The X-wing's three-row counterpart. When a digit's possible cells across three rows fall in the same three columns, that digit can be eliminated from those columns elsewhere.

    Techniques
  • 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.

    Rules & terminology
  • 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°.

    Techniques
  • XYZ-wing

    A three-cell wing pattern where the pivot has three candidates and each wing has two — eliminating the shared candidate from any cell that sees all three.

    Techniques
  • Y-wing (XY-wing)

    Three bivalue cells where the pivot shares one candidate with each wing — eliminating the third candidate from any cell that sees both wings.

    Techniques