Remote Pairs

Remote Pairs are a special case of XY-Chains where all cells in the chain have the same two candidates. This creates a distinctive pattern that's easier to spot and understand.

What are Remote Pairs?

Remote Pairs occur when:

Multiple cells have the identical bi-value candidates (e.g., all have [3,7])
These cells form a connected chain (each sees at least one other)
The chain has an even number of cells

The name: The cells are "pairs" (same two candidates) that can be "remote" from each other across the grid.

The Pattern

Consider four cells, all with candidates [3,7]:

Cell A: [3,7] ─── Cell B: [3,7] ─── Cell C: [3,7] ─── Cell D: [3,7]

Each cell sees the next in the chain (same row, column, or box).

The Logic

In a chain of identical pairs, colors alternate:

A[3,7] ─── B[3,7] ─── C[3,7] ─── D[3,7]
  Blue     Green      Blue      Green

Why alternating?

If A = 3, then B ≠ 3 (they see each other), so B = 7
If B = 7, then C ≠ 7, so C = 3
If C = 3, then D ≠ 3, so D = 7
Pattern: 3, 7, 3, 7 or 7, 3, 7, 3

Key insight: Cells at even distances apart have opposite values. Cells at odd distances have the same value.

Elimination Rule

With an even-length chain:

Same-colored cells (same position in chain) will have the same digit.

Any cell that sees TWO cells of the same color can have both candidates eliminated:

It sees a 3 and a 7 (or 7 and 3), covering both candidates
Either way, it can't be 3 or 7

Or equivalently: Any cell that sees cells at positions 1 and 3 (or 2 and 4) in the chain can be eliminated.

Visual Example

        Col 1       Col 5       Col 9
Row 2:  A[3,7]

Row 5:              B[3,7]

Row 8:                          C[3,7]

Row 9:              D[3,7]

Chain connections:

A → B (different box, share some unit? Let's say A and B share box or column)

Actually, let me make a cleaner example:

        Col 1       Col 4       Col 7
Row 1:  A[3,7]      B[3,7]
Row 4:              C[3,7]
Row 7:              D[3,7]      E[3,7]

Connections:

A and B: same row (row 1)
B and C: same column (column 4)
C and D: same column (column 4)
D and E: same row (row 7)

Chain: A ─ B ─ C ─ D ─ E (5 cells, odd length)

For even length, take A ─ B ─ C ─ D (4 cells):

Colors:

A: Blue
B: Green
C: Blue
D: Green

Elimination: A cell that sees both A (Blue) and C (Blue):

A is in row 1, col 1
C is in row 4, col 4
Cell R1C4 = B (already in chain)
Cell R4C1 sees A (col 1) and C (row 4) — check if it has [3,7]

If R4C1 has candidate 3 or 7, it sees A and C (both Blue). Eliminate 3 and 7!

Remote Pairs Characteristics

Why "Remote"?

The key cells for elimination might be far apart in the chain:

Cell 1 and Cell 3 are "remote" from each other
Yet they share the same polarity
A cell seeing both gets squeezed

Chain Length Requirements

Minimum: 4 cells (to have two same-color pairs)

Odd length (3, 5, 7...): The endpoints have the same color. Cells seeing both endpoints can be eliminated.

Even length (4, 6, 8...): More complex. Look for cells seeing non-adjacent same-colored cells.

Strong vs. Weak Links

In Remote Pairs:

All links are weak (cells just need to see each other)
But the internal constraint of bi-value cells creates alternation
No need for strong links in units — the identical candidates do the work

Finding Remote Pairs

Step 1: Spot Identical Bi-Value Cells

Scan for cells with the same two candidates. Mark them.

Step 2: Check Connectivity

Do these cells see each other? Build the chain:

A sees B (same row)
B sees C (same column)
C sees D (same box)
etc.

Step 3: Determine Colors

Assign alternating colors along the chain.

Step 4: Find Elimination Targets

Cells that see two same-colored cells. They can have both candidates eliminated.

Worked Example

Cells with [2,9]:

R1C2: [2,9]
R1C7: [2,9]
R4C7: [2,9]
R4C4: [2,9]
R7C4: [2,9]
R7C1: [2,9]

Build chain:

R1C2 ─── R1C7 ─── R4C7 ─── R4C4 ─── R7C4 ─── R7C1
 (A)      (B)      (C)      (D)      (E)      (F)
Blue    Green     Blue    Green     Blue    Green

Connections:

A-B: row 1
B-C: column 7
C-D: row 4
D-E: column 4
E-F: row 7

Same-colored pairs:

Blue: A(R1C2), C(R4C7), E(R7C4)
Green: B(R1C7), D(R4C4), F(R7C1)

Find elimination targets:

Cell that sees A and C:

A is R1C2, C is R4C7
R1C7 = B (in chain)
R4C2 sees A (column 2) and C (row 4). If R4C2 has [2,9], eliminate!

Cell that sees A and E:

A is R1C2, E is R7C4
R1C4 sees A (row 1) and E (column 4). If it has [2,9], eliminate!
R7C2 sees A (column 2) and E (row 7). If it has [2,9], eliminate!

And so on for other same-color pairs.

Remote Pairs vs. General XY-Chains

Aspect	Remote Pairs	XY-Chains
Candidates	All same pair	Can vary
Recognition	Easier	Harder
Links	All weak	Weak between cells
Coloring	Clear alternation	Implicit

Remote Pairs are a subset of XY-Chains where the chain happens to have identical bi-value cells throughout.

Common Mistakes

Mistake 1: Cells don't actually see each other

Just having the same candidates isn't enough. Each cell must see the next in the chain.

Mistake 2: Wrong color assignment

Colors must alternate. Don't skip cells or assign same color to adjacent cells.

Mistake 3: Eliminating from chain cells

The elimination targets are cells OUTSIDE the chain that see same-colored chain cells.

Mistake 4: Missing chain extensions

The chain might be longer than you initially see. Always look for more cells with the same pair.

Quick Reference

Remote Pairs definition:

Multiple cells with identical bi-value candidates
Cells form a connected chain
Colors alternate: Blue, Green, Blue, Green...

Elimination rule:

Find cells outside the chain
If a cell sees two same-colored chain cells
Eliminate both candidates from that cell

Finding them:

Identify cells with identical bi-value candidates
Check if they form a connected chain
Assign alternating colors
Find external cells seeing same-colored pairs

Requirements:

At least 4 cells for meaningful eliminations
Chain must be connected (each cell sees at least one neighbor)
Same two candidates in ALL chain cells