Sudoku Solver

Expert

Remote Pairs

A chain of cells containing the same pair of numbers. If the chain is long enough, the ends eliminate candidates.

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

8
1 2 3 4 5 6 7 8 9
9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
2
1 2 3 4 5 6 7 8 9
7
1 2 3 4 5 6 7 8 9
7
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
5
1 2 3 4 5 6 7 8 9
6
1 2 3 4 5 6 7 8 9
8
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
9
1 2 3 4 5 6 7 8 9
4
1 2 3 4 5 6 7 8 9
1
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
7
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
8
1 2 3 4 5 6 7 8 9
3
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
2
1 2 3 4 5 6 7 8 9
7
1 2 3 4 5 6 7 8 9
1
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
8
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
5
1 2 3 4 5 6 7 8 9
6
1 2 3 4 5 6 7 8 9
5
1 2 3 4 5 6 7 8 9
7
1 2 3 4 5 6 7 8 9
8
1 2 3 4 5 6 7 8 9
9
1 2 3 4 5 6 7 8 9
4
1 2 3 4 5 6 7 8 9
3
1 2 3 4 5 6 7 8 9
1
1 2 3 4 5 6 7 8 9
2
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
8
1 2 3 4 5 6 7 8 9
1
1 2 3 4 5 6 7 8 9
2
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
5
1 2 3 4 5 6 7 8 9
7
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
4
1 2 3 4 5 6 7 8 9
5
1 2 3 4 5 6 7 8 9
7
1 2 3 4 5 6 7 8 9
8
1 2 3 4 5 6 7 8 9
1
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
4
1 2 3 4 5 6 7 8 9
3
1 2 3 4 5 6 7 8 9
9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
7
1 2 3 4 5 6 7 8 9
8
1 2 3 4 5 6 7 8 9
2
1 2 3 4 5 6 7 8 9
5
1 2 3 4 5 6 7 8 9
6
1 2 3 4 5 6 7 8 9
2
1 2 3 4 5 6 7 8 9
6
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
5
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
9
1 2 3 4 5 6 7 8 9
1
1 2 3 4 5 6 7 8 9
7
1 2 3 4 5 6 7 8 9
8
1 2 3 4 5 6 7 8 9

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}:

  1. 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).
  2. 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.
  3. 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.
  4. 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

  1. Find Pairs: Look for multiple cells that contain the exact same two candidates (e.g., {3, 4}).
  2. Build a Chain: Connect them if they see each other.
  3. Count Steps: Find a chain with an Even Number of cells (4, 6, 8...).
  4. Check Ends: Ensure the Start and End cells are not in the same unit (otherwise they would eliminate each other directly).
  5. 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.