VWXYZ-Wing
A VWXYZ-Wing is an ALS-XZ construction involving exactly five distinct cells and five distinct candidate digits across two almost locked sets. For non-overlapping sets, the cell-count split is 4+1 or 3+2. The sets share a restricted common candidate X: every X occurrence in one set sees every X occurrence in the other, so X cannot occur in both sets. Any other shared digit Z can be eliminated from an outside cell that sees every Z occurrence in both sets.
What is a VWXYZ-Wing?
An almost locked set (ALS) consists of k unsolved cells in a single house — a row, column or box — whose combined candidates contain exactly k+1 distinct digits. A VWXYZ-Wing is the five-cell, five-digit specialization of the ALS-XZ rule: together, its two ALSs contain exactly five distinct cells and five distinct candidate digits. For non-overlapping ALSs, the possible cell-count splits are 4+1 — a four-cell ALS and a bivalue cell — or 3+2 — a three-cell ALS and a two-cell ALS. This walkthrough uses the 4+1 form. Other two-ALS constructions may still satisfy the ALS-XZ rule, but they are not VWXYZ-Wings unless they contain exactly five distinct cells and five distinct candidate digits.
How to spot it
Identify ALS A and ALS B whose cells total exactly five and whose union holds exactly five distinct digits. List each set’s candidates and find a shared digit X for which all X occurrences in A see all X occurrences in B. Then find another shared digit Z. A proposed target is valid only when it sees every Z occurrence in both sets. Do not require every cell in one ALS to see every cell in the other.
The logic
X cannot occur in both ALSs, so at least one ALS does not use X. Without X, that ALS has exactly as many remaining candidate digits as cells and must use every one of them, including Z. Therefore Z occurs in at least one of the two ALSs. Any outside cell that sees every Z occurrence in both sets cannot contain Z.