Remote Pairs in Sudoku: How the Chain Works and Why It’s Rare

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Published April 17, 2026 · Updated October 14, 2026

Take puzzle 786 of our Evil sudoku bank: 27 digits to begin with. Eleven naked singles, twelve hidden singles and two naked pairs later, 31 squares are still empty, and six of them hold exactly the same two candidates, 5 and 6. They line up: each shares a row, column or box with the next. That is a remote pair, and it takes the 5 and the 6 out of two more squares at once, leaving both of them a 7.

It is also one of the rarest moves you can learn. We played all 5,000 puzzles in our Evil bank with 23 techniques, always taking the simplest one available, and a remote pair was the move on two of them. Puzzle 786 is one. Below: how the chain works on that board, why it so seldom comes up, and what finds the same move in our Sudoku Helper, which has no remote-pair search at all.

What is a remote pair in sudoku?

A remote pair is a chain of cells that all hold exactly the same two candidates, say 5 and 6, where each cell sees the next: the two share a row, a column or a box. Two cells that see each other can’t hold the same digit, so the digits alternate along the chain. If the first cell is 5, the second is 6, the third 5, and so on; if the first is 6, everything flips. Either way, two chain cells an odd number of steps apart hold one 5 and one 6 between them, so a cell that sees both of them can hold neither.

The name comes from the pair. A naked pair locks two digits into two cells of one house; a remote pair locks them into two cells that need not share a house at all. In chain terms it is an XY-chain whose cells all hold the same pair. An XY-chain proves one digit at a time; with every cell alike, a remote pair proves both at once.

How does a remote pair remove candidates?

Back to puzzle 786 after its 25th move. The six cells holding only 5 and 6 are R8C7, R4C7, R4C6, R3C6, R1C4 and R9C4, in that order, and each sees the next through column 7, row 4, column 6, box 2 and column 4. Colour them alternately: the green cells (R8C7, R4C6, R1C4) hold one digit and the blue cells (R4C7, R3C6, R9C4) the other.

The ends, R8C7 (green) and R9C4 (blue), are five steps apart, so one is 5 and the other 6. R8C7 sits in row 8 and box 9, R9C4 in row 9 and box 8, so the cells seeing both are R8C4 to R8C6, the part of row 8 inside box 8, and R9C7 to R9C9, the part of row 9 inside box 9. Two of those six are empty. R8C5 and R9C9 both hold 5, 6 and 7, lose the 5 and the 6, and are left with 7: two naked singles from one move.

Two near misses show the rule at work. R8C8 and R9C5 hold 5, 6 and 7 too, but R8C8 sees only R8C7 and R9C5 sees only R9C4, so they keep their marks. And the chain needs all six cells: no four-cell stretch of it clears anything, because no cell holding a 5 or a 6 sees both ends of one.

Which cells does a remote pair clear, and which only look like it?

A target has to see two chain cells an odd number of steps apart, three or more. The ends are the obvious pair to try, but on a six-cell chain cells 1 and 4, 2 and 5, and 3 and 6 are three steps apart too.

A cell beside two neighbouring chain cells is the trap. R4C6 and R4C7 are next to each other in the chain and share row 4, so nothing else in row 4 can be 5 or 6. True, but that is a naked pair, not a remote pair, and on puzzle 786 it had already been played at move 23 (column 4’s pair, R1C4 and R9C4, followed at move 25). Every two neighbours in a remote pair are a naked pair; only cells that see chain cells further apart are new.

If the two chain cells you pick see each other, they are just another naked pair. If they don’t, the cells that see both come in one of two shapes:

• The two share a band or stack but not a box, like R8C7 and R9C4: two strips of three cells, each in one cell’s row (or column) and the other’s box.
• The two in different bands and stacks: just two cells, where each one’s row meets the other’s column.

Is a remote pair just Simple Colouring?

Once the naked pairs are done, yes. Each link of the chain is two cells with the same pair in one house, a naked pair. After that pair has been played, the house holds 5 and 6 nowhere else, so the two cells are its only places for 5 and its only places for 6: a strong link on each digit. Strong links on one digit are exactly what Simple Colouring follows. So the chain is a colouring chain on 5 and another on 6, its ends take opposite colours, and every cell a remote pair clears sees both colours.

Puzzle 786 shows it happening. Its two naked pairs were made of chain cells: R4C6 and R4C7 in row 4, R1C4 and R9C4 in column 4. They cleared the other 5s and 6s from two of the chain’s houses, and the other three held 5 and 6 only in their chain cells already. Look at the 5s alone:

That is why our helper manages without a remote-pair search. Its hint at move 26 is Simple Colouring on 5 for R8C5 and R9C9; a second colouring on 5 and one on 6 follow before the two 7s appear. Three hints for one remote pair, but the remote pair is the easier to see: every cell in it shows the same two marks, where colouring makes you trace one digit house by house.

We checked the claim at every position in our 5,000 Evil puzzles with a remote pair on the board and no single or naked pair left: 514 of them. At every one, each link of every remote pair was a strong link on both its digits, with the ends on opposite colours. Our helper’s Simple Colouring has a move at all 514; until October 2026 it missed three, where the cell to clear also sat in a second colouring chain on the same digit. And at all 1,146 positions with a remote pair on the board and no single left, every candidate a remote pair removed was one our XY-chain detector removes too.

Is a four-cell remote pair a W-Wing?

Yes, once the naked pairs are done. Call the four cells A, B, C and D. After the naked pair B–C is played, their house holds each digit only in B and C, a strong link. A and D hold the same pair, A sees B and D sees C. That is a W-Wing: matching two-candidate cells, A and D, bridged by the strong link B–C, each end of which one of them sees. Puzzle 4942 has one, 44 moves in.

The helper’s hint on that board is this W-Wing (“Step 45: W-Wing found”), with the same two end cells and the same 8 struck from R2C2, which is left as a 5. Read as a remote pair or as a W-Wing, the four cells prove the same thing; our 23-technique list tries W-Wings before remote pairs, so it plays the W-Wing too. At all 460 positions in our Evil bank where a four-cell remote pair sat on the board with no single or naked pair left, the helper had a W-Wing to offer. A remote pair only does something the wings can’t when it has six cells or more, and both of the remote pairs our solver needed had six.

How often do you need a remote pair?

For these counts the helper’s eighteen techniques were joined by five it lacks, Remote Pairs among them, and played puzzles from our own levels simplest move first; a puzzle counts if a remote pair was ever the move. We tried it just before Simple Colouring; placed after it, for the reasons above, it would almost never get a turn.

• Our classic game: never. None of our 800 test boards, Easy, Medium, Hard and Expert at 200 apiece, needed it. Every board there has to be solvable by singles (with locked candidates on Hard, naked pairs on Expert) before we deal it. The pattern does appear, on 28, 64, 68 and 77 of the 200 boards at some point, but something simpler always came first.
• Evil: 2 of 5,000. Both come from outside the first 500, which the bank’s score order makes harder than the whole: puzzle 786 above and puzzle 2693, whose six-cell chain on 1 and 2 removes a 2 from R8C8 and leaves it a 5.

So the pattern turns up far more often than it is needed. Across the 5,000 Evil puzzles, a remote pair that would remove something sat on the board at 1,146 positions with no single left. At all but two, something earlier on our list came first:

All 5,000 Evil puzzles, played with our 23 techniques (the helper’s eighteen plus Finned X-Wing, Finned Swordfish, Remote Pairs, 3D Medusa and Sue de Coq), simplest first. A position counts when no single was left and at least one remote pair would have removed a candidate. Measured October 2026.

Stuck with several cells showing the same two digits?

That is the board where a remote pair could be hiding. Work through it in this order:

1. Play the naked pairs first. Any two of those cells that see each other are a naked pair: clear their shared house.
2. Group the rest by pair. You need four or more cells with the same two candidates. With fewer, look elsewhere.
3. Trace the chain and count steps. Join cells that see each other, pick two that are an odd number of steps apart, and look where their rows, columns and boxes cross. Work from complete pencil marks: if a 7 was never written into a cell, its {5,6} proves nothing.
4. Check the length. Four cells is a W-Wing as well. Six or more, with nothing simpler on the board, and it is your move.

If your two-candidate cells hold different pairs, the general form is the XY-chain. For a single digit, try Simple Colouring or an X-cycle; to colour several digits at once, 3D Medusa. All of them are ranked in our guide to sudoku techniques.