XY-Chain practice sheets
A line of two-candidate cells, each forcing the next, ending on the digit it started with. Every sheet here needs at least one.
The move that needs a pencil
An XY-Chain is a run of cells that each hold exactly two candidates. Each cell shares one digit with the next and can see it. When the two ends turn out to carry the same digit, that digit has to sit in one of them — so it comes off anything that sees both ends.
The reason it is on a printed sheet rather than in an article is that the article can show you one chain, and a sheet can show you twenty. Spotting a chain is not a moment of insight; it is a habit of checking "does this pair lead anywhere" until it does.
Why a dedicated sheet
On a mixed board you meet an XY-Chain at the exact point where everything cheaper has failed, which is the worst possible moment to learn it — you are already tired and already suspicious that you have missed something simpler. Here every puzzle is built so that a chain exists, and the only question is where it starts.
Every puzzle is generated and then replayed with the cheapest technique first; it is kept only if an XY-Chain 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 XY-Chain, and nothing on the sheet asks for a tier above it. Chains are near the top of the ladder, so anything else you meet on the page will be something you already know.
Making the search mechanical
- Collect the bivalue cells. Every cell with exactly two candidates is a possible link. In a hard board there are usually ten to fifteen of them.
- Build from a pair, in both directions. Take one cell and ask which neighbours share one of its two digits. Then carry the other digit forward and repeat.
- Stop when the carried digit reappears at the start. That is the only condition that makes the chain do any work. A chain that wanders and stops proves nothing.
- Look for what sees both ends. If nothing is visible from both ends, the chain is real but has no target yet — keep it, and check again after the next move.
Step 2 is where most players lose the thread: they hop two cells, lose track of which digit they are carrying, and start again. Write the carried digit down.
Printing it
Scale 100%, A4 or Letter. Candidate marks on is mandatory — the technique is defined entirely in terms of two-candidate cells, and without marks there is nothing to see. One puzzle per page is the version to learn on; four per page is the version to drill.
Related practice
The full guide to XY-Chain walks a real four-cell chain, including the branch you have to check first. W-Wing is the nearest neighbour on the ladder — same "two identical pairs" idea, but the connection is a strong link rather than a chain.
Other sheets: X-Wing, skyscraper, swordfish.