W-Wing practice sheets

The pattern that connects nothing

A W-Wing is two cells with the identical two-candidate list — {2, 3} and {2, 3} — that cannot see each other. On their own they are inert. Two identical pairs sitting in different rows, columns and boxes tell you precisely nothing.

What brings them to life is a strong link on one of the two digits: a row, column or box where that digit has exactly two homes, one visible from each pair. Then one of the two pairs must take the other digit, and any cell that sees both of them loses it.

The reason this belongs on its own sheet is the search direction. Almost every other technique is found by following a line or a box. A W-Wing is found by grouping cells by their candidate pair and then looking outward for a link — a move that no amount of scanning rows and columns will teach you.

Why a dedicated sheet

In a mixed set, W-Wings arrive late. By the time one is the next move, the board has been reduced to a scatter of bivalue cells and the obvious patterns are all gone — which is exactly the state where players stop trusting themselves and guess.

Here the board is built around it. You know the pair is there, so the work becomes mechanical instead of hopeful: list the bivalue cells, group them, and hunt the link.

Every puzzle is generated and then replayed with the cheapest technique first; it is kept only if a W-Wing appears on that path. The filter runs in your browser, so the set is new on every visit.

What the grader guarantees

Every puzzle needs at least one W-Wing. Nothing on the sheet asks for a technique more than one tier above it, and W-Wing sits at the top of the ladder — so the hardest extra step you can meet is a forcing chain. That is expected rather than a defect: the sheet is a W-Wing drill, and a board that is only a W-Wing is usually too easy to be worth printing.

Making the search mechanical

1. Finish the pencil marks first. A W-Wing is defined entirely in two-candidate cells, so a half-marked board hides it. Turn candidate marks on for the first pass at least.
2. List the bivalue cells. Every empty cell with exactly two candidates. There are usually a dozen or fewer, and this inventory is the whole raw material.
3. Group them by pair. Two cells carrying the same {2, 3} is the starting shape. Cells that can see each other are just a naked pair — skip those, the W-Wing case is the pair that is blind.
4. Hunt the link, one digit at a time. Take 3 and look for a line where it has exactly two homes, one visible from each of your two cells. Then take 2 and do it again — the link often exists on the other digit of the pair.
5. Collect the eliminations. Every cell seeing both pairs loses the other digit. Usually that is one cell, occasionally two. One candidate is enough to unlock a board.

Printing it

Scale 100%, A4 or Letter. Candidate marks on is close to mandatory — without them the pattern is invisible, and this is the technique where marking first pays off most. One puzzle per page to learn on, four per page to drill.

Related practice

The full guide to W-Wing walks a real position step by step, including which end of the link each pair has to see — the part that is easiest to get backwards. XY-Wing is the three-cell version of the same "one of these must be Z" argument, and XY-Chain is what you get when the link becomes a chain.

Other sheets: XY-Wing, skyscraper, X-Wing, swordfish.