Remote Pairs
A chain of identical two-candidate cells colours into two answers.
Remote pairs is a chain of cells that every single one of them holds the same two candidates — a naked pair repeated across the grid. Because each link forces its neighbour to take the opposite digit, the two values alternate down the chain like colours on a checkerboard. The remote pairs sudoku technique then hunts for any cell outside the chain that can see both of its ends: since those ends are guaranteed opposite digits, one of them supplies each value, so the outside cell can safely drop both candidates.
Worked example
Here R1C1, R1C6, R6C6 and R6C1 all read exactly {1,2}, linked into a chain: R1C1-R1C6 share row 1, R1C6-R6C6 share column 6, and R6C6-R6C1 share row 6. Colour them alternately and the chain carries a 1 and a 2 in strict alternation. Now look at R1C2={1,7}: along row 1 it sees R1C1 and R1C6, two chain cells of opposite colour, so exactly one of that pair must be the 1. That places a guaranteed 1 in row 1 whichever way the chain falls, so R1C2 cannot also be a 1 — it collapses to 7.
When to use it
Reach for remote pairs once several cells share the same bivalue pair — say three or four cells all showing {1,2}. Trace a chain hopping between those identical cells wherever two of them share a row, column or box, then colour it alternately so the digits swap at every step. Finally scan for any cell that sees two chain cells an even number of links apart, because those two are opposite colours and pincer a guaranteed digit.
How to use it
- Find a chain of identical pairs. Locate four or more cells that all carry the exact same two candidates, each linked to the next because they share a row, column, or box.
- Colour the chain. Tag the cells alternately with two colours along the chain. One colour will end up holding the first digit and the other the second — you do not yet know which way round.
- Eliminate from cells seeing both colours. Whatever the orientation, any outside cell that sees a cell of each colour sees both digits, so remove both of those candidates from it.
Frequently asked questions
What is a Remote Pairs in Sudoku?
Remote pairs is a solving technique built on a chain of cells that all contain the identical two candidates. Each link forces its neighbour to the opposite digit, so the two values alternate along the whole chain. Any cell that can see both ends of the chain — which are guaranteed to be opposite digits — cannot hold either candidate. In the example, the {1,2} cells R1C1, R1C6, R6C6 and R6C1 let R1C2 shed its 1 and become 7.
How do I spot a remote pairs chain?
Start by finding several cells that share the same bivalue pair, such as {1,2}. Link them into a chain wherever two of them share a row, column or box, then colour the chain alternately so the two digits swap at every step. Any outside cell that sees two chain cells of opposite colour is your elimination target — that is how R1C2 in the worked grid, seeing R1C1 and R1C6 along row 1, loses its 1 and resolves to 7.
How is remote pairs different from a naked pair?
A naked pair is just two cells sitting in a single unit that share the same two candidates, letting you clear those digits from the rest of that one unit. Remote pairs strings four or more identical bivalue cells into an alternating chain that can span the whole board. Instead of clearing one unit, it eliminates from any cell that sees both ends of the chain — as R1C2 does with the four {1,2} cells at R1C1, R1C6, R6C6 and R6C1 above.