Remote Pairs is an advanced Sudoku technique based on chains of bivalue cells that all contain the same two candidates. When multiple cells each have exactly the same pair of candidates (say {A, B}) and they form a connected chain where each consecutive cell sees the next, alternating logic applies: if the first cell is A, the second must be B, the third must be A, and so on. Cells that are an even number of links apart in the chain must contain different digits.
The key elimination comes from this alternating property. Consider two cells in the chain that are an even number of links apart — one must be A and the other must be B. Together, they account for both values of the pair. Any cell outside the chain that can see both of these even-distance cells and contains candidate A or B can have those candidates eliminated, because A and B are fully accounted for by the two chain cells.
Remote Pairs is particularly powerful in puzzles where many bivalue cells share the same candidate pair, which happens more often than you might expect in hard and very hard puzzles. The technique can produce sweeping eliminations across the grid when the chain is long enough. It is conceptually related to Simple Coloring (which works on a single candidate) and XY-Chains (which work on multiple different pairs). Understanding Remote Pairs solidifies your grasp of how parity and alternating logic apply in Sudoku chains.
Try It Yourself
Walk through each step of the remote pairs technique on a real puzzle. Follow the instructions and try entering the correct value when prompted.
Look for bivalue cells sharing the same candidate pair. Cells (0,0), (0,3), (1,3), and (2,3) all contain candidates {2, 4}. They form a connected chain where each sees the next.
Step-by-Step Guide
Identify all bivalue cells in the grid and group them by their candidate pairs.
Find a group of three or more cells that all share the exact same two candidates (e.g., all have {A, B}).
Check if these cells form a connected chain where each cell sees the next cell in the chain.
Number the cells in the chain starting from 1. Cells at positions 1, 3, 5, ... are odd; cells at 2, 4, 6, ... are even.
For any two cells an even number of links apart (e.g., cell 1 and cell 3, or cell 2 and cell 4), note that one must be A and the other B.
Eliminate candidates A and B from any cell outside the chain that can see both of those even-distance cells.
Check the grid for new singles or further deductions.
Think of a chain of dominoes where every other one falls the same way — if you know any two dominoes an even number apart, they always show opposite faces, blocking those values for any bystander watching both.
Each consecutive pair in the chain forms a naked pair within their shared unit, forcing them to hold opposite values of {A, B}. This propagates strict alternating parity along the entire chain: odd-indexed cells all hold one value and even-indexed cells hold the other. Two cells an even number of links apart therefore must hold different values, collectively covering both A and B. Any external cell that sees both such cells is constrained by two simultaneous unit-exclusion rules — one forbidding A, the other forbidding B — eliminating both candidates.
When to use: Use Remote Pairs when you notice three or more bivalue cells all containing the same two candidates, connected in a chain where each cell sees the next. The longer the chain, the more eliminations you can find.
Common Mistakes to Avoid
Trying to apply the technique when the bivalue cells do not all share the exact same two candidates.
Every cell in the Remote Pairs chain must contain the identical pair of candidates. If any cell has a different pair, the chain breaks and the logic does not hold.
Eliminating based on cells an odd number of links apart instead of even.
Cells an odd number of links apart might contain the same digit. Only cells an even number of links apart are guaranteed to contain different digits, enabling eliminations.
Missing that each consecutive cell in the chain must directly see the next cell (share a row, column, or box).
The chain requires strong visibility between consecutive cells. If two cells cannot see each other, they cannot be consecutive links in the chain.
More Examples
See remote pairs applied in different puzzle configurations to strengthen your pattern recognition.
Remote Pairs Chain on Digits 5 and 7
Highlighted cells show the remote pairs pattern
Practice Puzzles
Apply the remote pairs technique on these mini challenges. Tap a highlighted cell and enter the correct digit.
Quick Reference
- Pattern:
- A chain of bivalue cells with the same two candidates, alternating along shared units
- Action:
- Eliminate both candidates from cells that see both ends of an even-length chain
- Look for:
- A sequence of cells all containing the same two candidates