BUG and larger ALS wings

BUG uniqueness deductions and five-to-seven-cell ALS-XZ wings and double-linked rings. These are separate logical families collected at a similar study level.

BUG Type 1

One guardian candidate prevents the verified BUG state and must be kept.

BUG Type 2

Several BUG exception cells share a guardian digit that can eliminate from their common peers.

BUG Type 3

BUG values combine with nearby cells to form a naked set in a shared house.

Two highlighted BUG cells lock candidates in a Sudoku row

BUG Type 4

Two BUG cells lock an additional candidate in their shared house.

VWXYZ-Wing

A single-linked five-cell almost-locked-set wing.

VWXYZ-Ring

The double-linked five-cell form with two restricted commons.

UVWXYZ-Wing

A single-linked six-cell almost-locked-set wing.

UVWXYZ-Ring

The double-linked six-cell form with two restricted commons.

TUVWXYZ-Wing

A single-linked seven-cell almost-locked-set wing.

TUVWXYZ-Ring

The double-linked seven-cell form with two restricted commons.

BUG deductions and larger almost locked sets

A Bivalue Universal Grave (BUG) is a special endgame state in which every unsolved cell is bivalue and each remaining candidate is balanced within its rows, columns and boxes. Left unbroken, that structure would support more than one completion. BUG Types 1–4 examine the cells or candidates that disturb the balance and use the puzzle’s guaranteed uniqueness to determine a placement or elimination.

The larger wing and ring guides develop almost-locked-set (ALS) reasoning beyond WXYZ constructions. VWXYZ, UVWXYZ and TUVWXYZ structures contain five, six and seven cells respectively. In a wing, one restricted common links the component sets; in a ring, two restricted commons create a doubly linked structure and often broader eliminations. The names encode construction size, but size alone is not proof: the candidates must satisfy the ALS count, visibility and restricted-common conditions described in each guide.

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