Solving Tips
Sudoku Chute Remote Pairs Technique: Eliminating Candidates Using Pairs and Chutes
Chute Remote Pairs is a clever advanced Sudoku technique that combines the properties of pairs with the distribution patterns of Chutes (3 cells in a row/column within a box). By analyzing the relationships between three boxes in the same tower, we can eliminate candidates in cells that can see both pair cells.
Core Principle:
In three boxes of the same tower (called Box A, Box B, and Box C), if Box A and Box B each contain a cell with the same pair (e.g., {2,8}), and these two cells are not in the same row, we examine the Chute in Box C - the 3 cells in the row where neither pair cell is located. If the Chute lacks one candidate (e.g., 2), then that number must be in the rows containing the pair cells, forcing one of them to be the other number (e.g., 8). Conclusion: One of the two pair cells must be 8, so cells that can see both pair cells can eliminate 8.
In three boxes of the same tower (called Box A, Box B, and Box C), if Box A and Box B each contain a cell with the same pair (e.g., {2,8}), and these two cells are not in the same row, we examine the Chute in Box C - the 3 cells in the row where neither pair cell is located. If the Chute lacks one candidate (e.g., 2), then that number must be in the rows containing the pair cells, forcing one of them to be the other number (e.g., 8). Conclusion: One of the two pair cells must be 8, so cells that can see both pair cells can eliminate 8.
Before reading this article, we recommend understanding Sudoku naming conventions and the basics of Naked Pairs.
What is a "Tower" and "Chute"?
In Sudoku, a Tower (or Chute) refers to three boxes arranged horizontally or vertically:
- Horizontal Towers: Boxes 1-2-3 (rows 1-3), Boxes 4-5-6 (rows 4-6), Boxes 7-8-9 (rows 7-9)
- Vertical Towers: Boxes 1-4-7 (columns 1-3), Boxes 2-5-8 (columns 4-6), Boxes 3-6-9 (columns 7-9)
A Chute specifically refers to the 3 cells in a single row (or column) within a box that aligns with the tower direction. For example, in a horizontal tower, the 3 cells in row 3 of Box 3 form a Chute.
Example 1: Chute Remote Pairs in a Vertical Tower
Let's look at the first example, finding Chute Remote Pairs in a vertical tower (Boxes 3-6-9).
Figure 1: R3C7 and R7C8 both have the pair {2,8}, Box 6's column 9 (Chute) has no 2
Analysis Process
1
Find the pair cells: In the vertical tower (Boxes 3, 6, 9), R3C7 (Box 3) and R7C8 (Box 9) both have the pair {2, 8}.
2
Verify position relationship: R3C7 is in column 7, R7C8 is in column 8. They are not in the same column (this is the key condition).
3
Identify the Chute: The two pair cells are in columns 7 and 8, so the third box's (Box 6) column 9 (the column where neither pair cell is located) is the Chute, containing 3 cells.
4
Check the Chute: Box 6's column 9 (the Chute) has no candidate 2.
5
Reasoning process:
- Since the Chute has no 2, Box 6's digit 2 must be in column 7 or column 8
- If Box 6's 2 is in column 7 → R3C7 cannot be 2 (only one 2 per column) → R3C7 must be 8
- If Box 6's 2 is in column 8 → R7C8 cannot be 2 (only one 2 per column) → R7C8 must be 8
- Either way, one of R3C7 and R7C8 must be 8
6
Make eliminations: Since one of these cells must be 8, any cell that can see both cells cannot have 8.
Conclusion:
The Chute (Box 6, column 9) has no 2, therefore one of R3C7 and R7C8 must be 8. Cells that can see both can eliminate 8.
The Chute (Box 6, column 9) has no 2, therefore one of R3C7 and R7C8 must be 8. Cells that can see both can eliminate 8.
Example 2: Chute Remote Pairs in a Horizontal Tower
Now let's look at another example in a horizontal tower (Boxes 1-2-3).
Figure 2: R2C1 and R1C7 both have the pair {3,8}, Box 2's row 3 (Chute) has no 8
Analysis Process
1
Find the pair cells: In the horizontal tower (Boxes 1, 2, 3), R2C1 (Box 1) and R1C7 (Box 3) both have the pair {3, 8}.
2
Verify position relationship: R2C1 is in row 2, R1C7 is in row 1. They are not in the same row.
3
Identify the Chute: The two pair cells are in rows 1 and 2, so the third box's (Box 2) row 3 (the row where neither pair cell is located) is the Chute.
4
Check the Chute: Box 2's row 3 (the Chute) has no candidate 8.
5
Reasoning process:
- Since the Chute has no 8, Box 2's digit 8 must be in row 1 or row 2
- If Box 2's 8 is in row 1 → R1C7 cannot be 8 (only one 8 per row) → R1C7 must be 3
- If Box 2's 8 is in row 2 → R2C1 cannot be 8 (only one 8 per row) → R2C1 must be 3
- Either way, one of R2C1 and R1C7 must be 3
6
Make eliminations: Since one of these cells must be 3, any cell that can see both cells cannot have 3.
Conclusion:
The Chute (Box 2, row 3) has no 8, therefore one of R2C1 and R1C7 must be 3. Cells that can see both can eliminate 3.
The Chute (Box 2, row 3) has no 8, therefore one of R2C1 and R1C7 must be 3. Cells that can see both can eliminate 3.
Key Point: Missing Candidate ≠ Eliminated Candidate
Important Understanding:
A common point of confusion with this technique is that the candidate missing from the Chute and the candidate to eliminate are opposites!
A common point of confusion with this technique is that the candidate missing from the Chute and the candidate to eliminate are opposites!
- Chute missing 2 → One pair cell must be 8 → Eliminate 8
- Chute missing 8 → One pair cell must be 3 → Eliminate 3
How to Find Chute Remote Pairs
Finding Chute Remote Pairs requires a systematic approach:
1
Find pair cells: First, identify all bivalue cells (cells with exactly two candidates).
2
Look for matching pairs: In the same tower of three boxes, find two pair cells with identical candidates that are in different boxes.
3
Check positions: Verify these two pair cells are not in the same row (horizontal tower) or not in the same column (vertical tower).
4
Identify the Chute: Find the 3 cells in the third box that are in the row (or column) where neither pair cell is located.
5
Check the Chute: See if the Chute is missing one of the pair's candidates. If so, eliminations can be made.
6
Make eliminations: Eliminate the other candidate from cells that can see both pair cells.
Important Notes:
- The two pair cells must be in different boxes
- The two pair cells cannot be in the same row (horizontal tower) or same column (vertical tower)
- When checking the Chute, consider filled digits and candidates (including pencil marks)
- If the Chute is missing both candidates, you can eliminate both candidates
Technique Summary
Key points for applying Chute Remote Pairs:
- Recognition: Two cells in different boxes of the same tower have identical pairs and are not in the same row/column
- Key location: The Chute - the row/column in the third box where neither pair cell is located
- Trigger condition: The Chute is missing one of the pair's candidates
- Elimination logic: Chute missing A → Eliminate B; Chute missing B → Eliminate A
- Elimination scope: All cells that can see both pair cells
Practice Now:
Start a Sudoku game and try using Chute Remote Pairs! When you find two identical pair cells in different boxes of the same tower, remember to check the third box's Chute.
Start a Sudoku game and try using Chute Remote Pairs! When you find two identical pair cells in different boxes of the same tower, remember to check the third box's Chute.