Intersections, subsets and fish

Locked candidates, naked and hidden subsets, and fish described through their objects, base sectors and cover sectors.

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.

X-Wing

A two-row or two-column fish construction.

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 construction.

Candidate restrictions across Sudoku houses

A locked set balances N objects with N possibilities. In the RC view, N cells have a union of N candidate digits: a naked set removes those digits elsewhere in the sector. In the positional RN, CN, or BN views, N digits have a union of N positions in a row, column, or box: a hidden set removes other digits from those positions. Pointing and Claiming are size-one base-and-cover intersections.

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 construction’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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