What is a Remote Pair
A remote pair is a chain of bivalue (two-candidate) cells that all share the same two candidates. When the chain connects two cells that do not see each other, the chain induces a strong link for one of the candidates across the two ends. That lets you remove that candidate from any cell that can see both endpoints. The name comes from the fact that the two linked cells can be far apart on the grid — remote from each other — yet act like a linked pair.
How the logic works (plain explanation)
Each bivalue cell acts as a simple 'either-or' statement: if it isn't one candidate, it must be the other. When multiple such bivalue cells are arranged so that each is in the same house (row, column or box) with the next one, those either-or statements chain together. If the chain has the right length and structure, assuming one end is a given candidate forces a sequence of forced values that determine the candidate at the other end. When both ends are forced to the same candidate if one end takes it, you get a strong link on that candidate between the two ends. Any cell that sees both endpoints cannot contain that candidate because it would create a contradiction in the forced assignments.
When to look for a remote pair
- Scan bivalue cells during candidate marking: remote pairs start with multiple bivalue cells that share the same two numbers. If you spot a group of them, check how they connect by house.
- Look for chains that alternate houses (row to column to row, or column to box to column, etc.) and link distant cells that do not see each other directly.
- Use remote pairs when a candidate appears in a cell that sees both endpoints. That candidate is a target for elimination.
Remote pairs are most useful after basic scanning and candidate marking. They are a mid-level technique: not as rare as some advanced grid patterns, but they do require a clear candidate layout and a little patience to trace the chain.
Step-by-step: how to read the example grid
Below is a compact candidate-grid example you can follow. Five bivalue cells form a chain: A -> B -> C -> D -> E. Each of those five cells has exactly the same two candidates, 3 and 7. The chain links are as follows:
- A and B share row 1 (strong link between the two candidates within that row)
- B and C share column 5
- C and D share row 4
- D and E share column 8
Because there are five bivalue cells (an odd number of nodes), the parity of forced values makes the candidate 3 behave as a strong link between A and E: if A is 3 then the chain forces C and E to be 3 as well, and conversely if A is 7 the chain forces E to be 7. That means exactly one of A or E must be 3. Any cell that can see both A and E cannot therefore be 3 — if it were, it would conflict with the forced uniqueness created by the remote pair.
In the example, cell (1,8) sees A (same row 1) and E (same column 8). It currently includes candidate 3 among its possibilities. Because A and E form a remote pair on candidate 3, we can eliminate candidate 3 from cell (1,8).
Practical tips for using the remote pair sudoku technique
- Only use this when all involved cells are true bivalue cells with the same two candidates; if one of the chain cells contains a third candidate the logic is broken.
- Check houses carefully: each adjacent pair in the chain must share a house so the forced relationship holds.
- Tracing the chain on a candidate-marked grid helps: write small pencil marks and label the chain ends (A, B, C...) to avoid confusion.
- Remote pairs are easier to spot when you keep candidate marking tidy and avoid erasing all pencil marks prematurely.
- When you eliminate a candidate using a remote pair, update candidate lists — that elimination may generate new singles or new bivalue cells that lead to further progress.
Example walkthrough (use the visual)
Refer to the candidate-grid visual. The five highlighted bivalue cells are all {3,7}. The endpoints are marked A at (1,2) and E at (7,8). The target cell (1,8) contains candidate 3; because it sees both endpoints of the remote pair on candidate 3, you can remove 3 from (1,8) immediately. After removing it, check for new singles or chain opportunities that open up.
Summary
The remote pair sudoku technique is a useful mid-level method that turns a chain of identical bivalue cells into a strong link across distant cells. Look for identical two-candidate cells connected by shared houses; when the endpoints don't see each other, any candidate that is strongly linked across them can be removed from cells that see both ends. Keep candidate marks clean, label chains when needed, and use remote pairs to unlock stubborn candidate clutter.