Sudoku-YAdvanced
Remote Pairs: pass a pair along a chain
A repeated {2,9} pair can carry information without choosing which end is 2 first.
Every cell needs the same two candidates
Connect matching bivalue cells that see each other. Neighbors on the chain must take opposite values. An odd number of links makes the endpoints opposite, so together they contain both digits.
HoDoKu — Chains: links and inferences · SudokuWiki — Weak and Strong Links
Our four cells and three links
Let B2, H2, H8 and C8 all have {2,9}. Follow B2 → H2 → H8 → C8. Adjacent cells share a row or column. Starting with B2=2 gives 2 → 9 → 2 → 9; starting with B2=9 gives 9 → 2 → 9 → 2.
B7 sees B2 through row B and C8 through the top-right box. In either case it sees both a 2 and a 9 at the endpoints, so remove both candidates there. This is an original partial scenario.
Three cells do not give the same result
Stopping at H8 leaves two links, making B2 and H8 equal rather than opposite. They no longer reserve both digits. Count the links instead of simply spotting many similar cells.
An extra 6 candidate at H8 also interrupts the guaranteed alternation. It would require a different argument.
How this differs from a naked pair
A naked pair directly occupies one unit. Here intermediate cells establish opposite values at distant endpoints. Targets must see both endpoints; seeing one intermediate cell is insufficient.
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.
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A five-cell {2,9} chain has four links. Must its endpoints differ?
Show explanation
No. Four alternating links make the endpoints equal, so they do not jointly reserve both digits.
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