A chain of bivalue cells sharing the same two candidates, where alternating parity forces eliminations.
A Remote Pair is a chain of cells that all contain exactly the same two candidates. Each cell in the chain is connected to the next by sharing a row, column, or box. Because each cell must be one digit or the other, the chain creates an alternating pattern, like coloring cells in two colors.
Any cell outside the chain that can see chain cells of both parities (both colors) cannot contain either digit, one color holds one digit and the other holds the other, so both are accounted for. This allows powerful eliminations from cells that intersect the chain at different-parity points.
Remote Pairs are one of the first chain-based techniques you'll encounter. They bridge the gap between basic subset techniques and more advanced coloring and chain strategies.
Find two or more cells that all contain exactly the same two candidates (a bivalue pair like {6, 9}). Verify they form a connected chain where consecutive cells share a unit (row, column, or box).
Assign alternating parity to each cell: the first is Color A, the second Color B, the third Color A again, and so on. Adjacent cells (different colors) must hold different digits. All cells of the same color hold the same digit from the pair.
Look for cells outside the chain that can see chain cells of both colors. Any such cell cannot contain either of the chain's digits, the two different-colored chain cells it sees must hold one digit each, covering both.
Example 1: Remote Pair Chain (4 cells)
Look at cells R3C9, R3C3, R8C3, and R8C8. Each contains exactly the same two candidates: {1, 3}. These cells form a Remote Pair chain: R3C9 and R3C3 share row 3, R3C3 and R8C3 share column 3, and R8C3 and R8C8 share row 8.
Color the chain alternately: R3C9 = Color A, R3C3 = Color B, R8C3 = Color A, R8C8 = Color B. The endpoints (R3C9 and R8C8) are different colors, so any cell seeing both has both digits accounted for.
R1C8 sees R3C9 (Color A, box 3) and R8C8 (Color B, column 8). R9C9 sees R3C9 (Color A, column 9) and R8C8 (Color B, box 9). Eliminate 3 from R1C8 and R9C9.
Example 2: Longer Remote Pair Chain (6 cells)
Now look at six bivalue cells with candidates {3, 6}: R4C7, R1C7, R1C9, R8C9, R8C6, and R5C6. They form a connected chain: R4C7 and R1C7 share column 7, R1C7 and R1C9 share row 1, R1C9 and R8C9 share column 9, R8C9 and R8C6 share row 8, and R8C6 and R5C6 share column 6.
Assign alternating colors: R4C7 = A, R1C7 = B, R1C9 = A, R8C9 = B, R8C6 = A, R5C6 = B. The endpoints R4C7 (A) and R5C6 (B) are different colors. R4C4 sees R4C7 (A, row 4) and R5C6 (B, box 5). R5C8 sees R4C7 (A, box 6) and R5C6 (B, row 5). Eliminate 6 from R4C4 and R5C8.
Explore all 28 solving techniques in our complete technique guide.