Intersections, subsets and fish

Elimination techniques based on locked candidates, naked and hidden subsets, and basic fish patterns (X-Wing, Swordfish).

Candidate 9 confined to one Sudoku box column, eliminating two other candidate 9s

Pointing

Box-to-line candidate restriction and elimination.

Candidate 7 confined to one Sudoku box within a row, eliminating four other candidate 7s

Claiming

Line-to-box candidate restriction and elimination.

Hidden Pair

Two digits restricted to two cells in one house.

A naked pair of candidates 1 and 2 eliminates those candidates from other cells in a Sudoku column

Naked Pairs

Two matching two-candidate cells that eliminate peers.

Four candidate 3s form an X-Wing across two rows and two columns in a Sudoku grid

Naked Triplet

Three cells containing only three combined candidates.

Hidden Triplet

Three digits confined to three cells in one house.

Swordfish

A three-row or three-column fish pattern.

Candidate restrictions across Sudoku houses

These strategies eliminate candidates by proving that a set of digits is confined to particular cells or houses. Pointing and Claiming, collectively known as locked candidates, use the overlap between a 3×3 box and a row or column. Naked and hidden pairs or triplets apply the same conservation principle inside one house: when n digits are restricted to n cells, those cells or digits can be separated from the remaining candidates.

X-Wing and Swordfish extend that logic across several rows and columns. An X-Wing confines one digit to the same two columns in two rows (or the transposed arrangement), while a Swordfish uses three base houses and three cover houses. The eliminations are valid because the selected digit must occupy the pattern’s cover positions. Studying these methods together makes the shared structure visible and prepares solvers for larger fish and more complex candidate networks.

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