WXYZ-Wing in Sudoku: A Practical Guide

Start with four cells and four candidates

A WXYZ-Wing is an advanced Sudoku pattern built from four cells containing exactly four candidates in total. The cells are usually spread across two units rather than sitting together as an ordinary naked quad. One useful way to learn the pattern is to begin with the classic narrow form: a hinge cell contains W, X, Y, and Z, while three related cells contain combinations such as WZ, XZ, and YZ. The important candidate is Z, which appears across the pattern in positions that are not all able to see one another. The other candidates are restricted more tightly inside shared rows, columns, or boxes. This geometry means that no matter which value eventually occupies the hinge, at least one Z in the pattern must be true. In Shapedoku, the same logic works with four shapes instead of four digits. Full Notes are essential because the pattern depends on knowing the complete candidate set of every participating cell. It is most appropriate on Extreme puzzles after singles, subsets, and simpler wings have already been checked.

Understand the non-restricted common candidate

The broader definition of a WXYZ-Wing is easier to use once you understand restricted and non-restricted candidates. The four cells contain four candidates in total and are arranged across two interacting Sudoku units. For three of those candidates, every occurrence inside the pattern can see every other occurrence of the same candidate because they share a row, column, or box. Those candidates are restricted. One candidate is different: at least two of its occurrences do not see each other. That candidate is the non-restricted common candidate and becomes the elimination value. Because the other candidates are confined by their shared units, the completed pattern must contain the non-restricted candidate in at least one of its possible pattern positions. Therefore, any outside candidate of that same value that sees every possible occurrence inside the WXYZ-Wing cannot be true. The key phrase is every possible occurrence. A target that sees only two or three of them is not safely eliminated. This visibility check is where many false WXYZ-Wings fall apart. Before making the elimination, also confirm that the four selected cells really contain only the four pattern candidates. A hidden fifth candidate breaks the structure.

Search for the pattern without testing every cell group

Do not try every combination of four unsolved cells. Start in areas with dense but orderly Notes. Look for a cell with three or four candidates, then inspect cells it can see for overlapping candidate sets. A possible four-cell group should contain no more than four candidates in total. Once you have a candidate group, check each symbol separately and ask whether all of its occurrences within the group see one another. If exactly one candidate is non-restricted, look for outside occurrences that see all of that candidate's positions in the pattern. Verify the union of candidates again before removing anything. If the four cells secretly contain a fifth candidate, the pattern is invalid. After a successful elimination, stop hunting WXYZ-Wings and return to simpler logic. One removed candidate may create a naked single, hidden single, pair, or strong link elsewhere. On Shapedoku, smart Note cleanup helps after final placements, but the initial WXYZ verification still depends on your candidate map being complete. Treat the technique as a precise tool for one difficult bottleneck, not as a pattern you must force onto every Extreme grid.

1. Find four cells whose combined Notes contain exactly four candidates.
2. Check how each candidate is distributed across rows, columns, and boxes containing the four cells.
3. Identify the one candidate whose pattern occurrences are not all mutually visible.
4. Find an outside occurrence of that candidate that sees every occurrence inside the WXYZ-Wing.
5. Remove only that outside candidate after verifying all four cell candidate lists.
6. Return to singles, subsets, and strong links before searching for another WXYZ-Wing.