XYZ-Wing practice sheets

The wing that is easier to learn than to find

XYZ-Wing has a reputation for being the wing nobody uses. The logic is short — one pivot holding three digits, two pincers holding two each, and whichever value the pivot takes, something in the pattern is the shared digit. But on a real board the pattern is thin: the elimination only reaches cells that see all three pattern cells at once, and there are usually not many of those.

That is the honest reason this sheet exists. Reading the proof once takes two minutes; recognising the shape on a board full of pencil marks takes repetition, and repetition needs boards where the pattern is actually there.

The shape, and the one constraint that matters

• Pivot — one cell with exactly three candidates, {X, Y, Z}.
• Pincer A — two candidates, {X, Z}. Both must come from the pivot's list.
• Pincer B — two candidates, {Y, Z}. Together with pincer A it must cover all three of the pivot's digits.
• Visibility — each pincer has to share a unit with the pivot. In most boards that means all three cells sit in one box, which is why every diagram draws it that way; a shared row or column satisfies the same requirement.
• Elimination — Z cannot appear in any cell that sees the pivot and both pincers.

The shared digit Z is the one both pincers have in common. Check that it appears in the pivot too — if it does not, you are looking at an XY-Wing, not this.

Why the box is not the requirement

A lot of guides state that all three cells must be in the same box. It is a useful habit while learning, and it is where the pattern usually turns up, but it is not what makes the logic work. What the proof needs is that pincer A cannot take X because the pivot might be X, and pincer B cannot take Y because the pivot might be Y. Both of those follow from the pincers seeing the pivot — nothing else.

Knowing this matters in one direction only: if you find three cells with the right candidate lists and the pivot sees both pincers through different units, it is a valid XYZ-Wing and worth acting on. Do not throw it away because it does not look like the picture.

What the grader guarantees

Every puzzle on this sheet needs at least one XYZ-Wing elimination, and nothing on it asks for more than one tier above: the hardest extra step you can meet is a swordfish, a W-Wing or a chain. The filter never relaxes to fill a sheet, so if one comes up short, press New set.

Expect these sheets to take a moment to build. XYZ-Wings are genuinely uncommon — the grader meets one in roughly one board in thirty of this depth — so filling seven puzzles means searching a few hundred boards. That is the filter working, not the page hanging.

Printing it

Scale 100%. Four puzzles per page gives 78 mm boards; two per page leaves room to write; one per page is a single hard puzzle to sit with.

Candidate marks are essential here. The pattern is defined entirely by candidate lists — a three-candidate cell and two two-candidate cells in the right arrangement — and you cannot see that arrangement without the marks in front of you. Start with marks on. Answer page adds the solutions at the end, numbered to match.

Where to go next

The full guide to XYZ-Wing has the three-case proof, a real board worked through to the two eliminations it produces, and a table setting it beside the XY-Wing so the two stop blurring together.

If the two-candidate version is not solid yet, do the XY-Wing sheet first — same idea, wider applicability, and it appears far more often. When three-cell patterns come easily, the natural step up is a chain: XY-Chain strings these cells together until the ends share a digit.