Remote Pair

Updated 15 October 2026

A Remote Pair is a chain of an even number of cells, each holding the same two candidates and each seeing the next: the digits alternate along the chain, so its two ends always take opposite digits, and any cell that sees both ends can hold neither.

How Suuudokuuu finds a Remote Pair

Suuudokuuu’s engine has no Remote Pair detector. A Remote Pair is an XY-Chain in which every cell happens to hold the same two digits, and the XY-Chain detector finds it and reports it under that name. One difference is worth knowing: an XY-Chain proves one digit at a time, so the engine reports the elimination of one of the pair’s digits per chain. The Remote Pair argument removes both, and the second set of eliminations is the same chain read in the opposite direction.

The logic is a row of naked pairs stretched across the board. Each cell is one digit or the other; two neighbours in the chain see each other, so they cannot be the same digit. Along the chain the digits therefore alternate, and with an even number of cells the first and last cells end up with different digits — together they use both. A cell that sees both ends sees both digits.

Worked example

The chain runs from r1c7 down column 7 to r9c7, across box 9 to r8c9, and up column 9 to r6c9: four cells, every one of them holding 6 and 8 and nothing else. Whichever digit r1c7 takes, r9c7 takes the other, r8c9 the first again and r6c9 the other, so the two ends hold one 6 and one 8 between them.

r1c9 shares row 1 with r1c7 and column 9 with r6c9; r4c7 and r6c7 share column 7 with r1c7 and box 6 with r6c9. All three see both ends, so none of them can be 6 — which is what the engine reports — and by the same argument none of them can be 8 either. r1c9 was carrying 2, 6 and 8, so the full Remote Pair leaves it a single.

How to spot a Remote Pair

1. Collect cells with the same pairLook for bivalue cells that carry exactly the same two candidates, such as several cells holding only 6 and 8.
2. Link them into a chainConnect cells that see each other through a row, column or box into a single path.
3. Count the cellsWith an even number of cells the ends hold opposite digits. With an odd number they hold the same digit, and the pattern does not apply.
4. Erase both digits where both ends are seenRemove both digits of the pair from every cell outside the chain that sees both ends.

Common mistakes

• Using an odd-length chain. Three or five cells leave the ends with the same digit, so nothing can be erased.
• Including a cell with a third candidate. Every link needs a cell that is exactly one of the two digits.
• Stopping at one digit. The pattern removes both digits of the pair from the cells that see both ends.

With three cells and three different digits the same idea becomes an XY-Wing. Every pattern the engine implements is on the technique index.