The Remote Pairs strategy is essentially a Simple Coloring chain, but strictly for cells that have the same two candidates.
It connects a pair of numbers (like 3 and 4) across the grid, even if they are far apart (hence "Remote").
Interactive Example
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Click "Apply Logic" to see the strategy in action.
Real Example Explanation
In the interactive example above, look at the cells with candidates {3, 4}:
- The Chain: We find a path of cells that contain only 3 and 4.
- Start: R1C4.
- Step 2: Connected to R5C4. (Strong link on the column).
- Step 3: Connected to R5C3. (Strong link on the row).
- End: Connected to R9C3. (Strong link on the column).
- The Count:
- The chain has 4 links (or 4 cells involved).
- Since it is an Even Number of steps, the colors "flip" an odd number of times.
- This means the Start (R1C4) and End (R9C3) must be opposites.
- The Logic:
- If R1C4 is 3 -> R5C4 is 4 -> R5C3 is 3 -> R9C3 is 4.
- If R1C4 is 4 -> R5C4 is 3 -> R5C3 is 4 -> R9C3 is 3.
- Result: One end is 3, and the other is 4. We don't know which is which, but we know they are different.
- The Elimination:
- Any cell that sees BOTH the Start (R1C4) and the End (R9C3) implies a contradiction.
- R1C3 sees R1C4 (in Row 1) and R9C3 (in Column 3).
- Therefore, R1C3 cannot be 3 (because of one end) AND cannot be 4 (because of the other). Both candidates are removed.
How to Spot It
- Find Pairs: Look for multiple cells that contain the exact same two candidates (e.g., {3, 4}).
- Build a Chain: Connect them if they see each other.
- Count Steps: Find a chain with an Even Number of cells (4, 6, 8...).
- Check Ends: Ensure the Start and End cells are not in the same unit (otherwise they would eliminate each other directly).
- Eliminate: Remove the pair values from any cell that sees both the Start and End.
Why "Remote"?
Usually, a "Naked Pair" requires the two cells to be in the same box, row, or column. Remote Pairs allows you to use the logic of a Naked Pair even when the cells are on opposite sides of the grid, connected by a chain.