Sudoku-YAdvanced
XY-Chains: change digits, then meet the same digit again
Unlike an X-Chain, this chain changes digits inside each cell before returning to the target digit.
A two-candidate cell passes the implication
Each XY-Chain cell has exactly two remaining candidates. Excluding one forces the other. Consecutive cells must see each other and share the linking digit. Useful endpoints contain the same target digit.
HoDoKu — Chains: links and inferences · SudokuWiki — XY-Chains
Our four original pairs
Use A1={2,4}, A5={4,7}, E5={7,9} and E8={2,9}. The route follows row A, column 5 and row E. Target A8 sees A1 and E8.
If A1 is not 2, it is 4; A5 then becomes 7, E5 becomes 9, and E8 becomes 2. If A1 is 2 instead, it blocks A8 directly. Either way, remove 2 from A8 without deciding which endpoint supplies it.
A third candidate opens a side route
Add 1 at E5, making {1,7,9}. After A5=7, E5 could be 1 rather than 9, allowing E8=9. Neither endpoint is then required to hold 2. Incomplete handwritten notes cannot establish the bivalue premise.
Write the digit, not just an arrow
“A1=4 makes A5≠4, so A5=7” records both the shared-unit exclusion and the two-candidate step. A line connecting two cells records neither on its own. Keep enough detail to retrace each link.
In Classic 9×9, use Scan to scan the current entries, inspect justified eliminations and open this lesson. Chain and ALS searches are bounded; UR Type 1 and BUG+1 require verified uniqueness. Reading this lesson never changes your saved game.
Try before looking
Try before revealing
Can you also remove 4 from A8 because it appears near the start of the chain?
Show explanation
Not from this proof. It guarantees a 2 at one of the endpoints, not a 4.
References and further reading
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