The Logic of Linear Convergence: A Deep Dive into Remote Chute Pairs

1. Introduction: The "Tunnel" Effect

While standard Sudoku strategies often focus on single houses (rows, columns, or boxes) or specific chains of candidates, Remote Chute Pairs (often called Chute Clams or Parallel Pair Analysis) leverage the structural geometry of the grid itself. The technique is a powerful intermediate-to-advanced strategy that exploits the alignment of "Chutes" (sets of three parallel rows or columns) to bypass standard visibility rules.

Fundamentally, a Remote Chute Pair pattern identifies a contradiction caused by two specific candidates in two specific cells that, while physically distant, are logically connected through the "tunnel" of a Chute. This connection allows for eliminations in cells that "see" both ends of this logical tunnel, effectively acting as a Teleporting Naked Pair.

2. Anatomy of the Grid: Defining Chutes

To understand this strategy, one must first visualize the grid as a collection of "Chutes" rather than just rows and columns.

2.1 The Concept of a Chute

• Horizontal Chute (Band)
  A set of three rows that encompass three entire 3x3 boxes (e.g., Rows 1-3).
• Vertical Chute (Stack)
  A set of three columns that encompass three entire 3x3 boxes (e.g., Columns 1-3).

3. The Logic of Remote Chute Pairs

The Remote Chute Pair strategy is essentially a Locked Candidates logic applied across the length of a Chute to form a virtual Naked Pair.

3.1 The "Simple" Remote Pair (Graph Theory)

Often, "Remote Pairs" refers to a chain of bivalue cells {X, Y} of even length.

• If the chain has an Even length (4, 6, 8...), the start and end cells effectively have opposite values.
• Conclusion: One of C1 or C4 MUST be a 1, and the other MUST be a 2.
• Elimination: Any cell that sees both C1 and C4 cannot contain 1 or 2.

4. Visualizing the Elimination

The power of the Remote Pair (specifically within a Chute or across the grid) lies in the "Pincer" effect.

5. Relation to Other Strategies

5.1 Remote Pair vs. Naked Pair

Naked Pair: Two cells in the same house with candidates {X, Y}. Immediate elimination.
Remote Pair: Two cells separated by a chain. They act as a Naked Pair affecting the cells that see both ends.

5.2 Remote Pair vs. XY-Chain

A Remote Pair is a specific subset of an XY-Chain. XY-Chains allow values to change ({1,2} to {2,3}), while Remote Pairs keep values static, allowing for dual elimination.

6. Summary of Rules