Solving Tips

Chute Remote Pairs Technique: Eliminate Candidates Using Pairs and Chute

2025-05-27 · 8 min read
Knowledge Base / Techniques Index / Chute Remote Pairs

Chute Remote Pairs is a clever elimination method among advanced Sudoku techniques. It combines the properties of pairs with the distribution patterns of Chute (3 cells in a row or column within a box in the tower) to eliminate candidates by analyzing the number relationships between three boxes in the same tower.

Core Principle:
In three boxes of the same tower, if two boxes each have a cell with the same pair (e.g., {3,6}), and these two pair cells are not in the same row (horizontal tower) or column (vertical tower), then we examine the 3 cells in the "third row/column" (the row/column where neither pair cell is located) in the third box, called the Chute. If the Chute doesn't contain a certain candidate (e.g., 3), then that number in the third box must be in the row/column where the pair cells are located, which causes one of the pair cells to not be that number and can only be the other number (e.g., 6). The final conclusion is: One of the two pair cells must be 6, therefore positions that can see both cells can eliminate 6.
Chute Remote Pairs Principle Animation
Chute Remote Pairs Principle Diagram: Same pairs in two boxes of the same tower, combined with missing number in Chute for elimination

Before reading this article, we recommend familiarizing yourself with Sudoku row/column/box naming conventions and the basic concept of the Pair method.

What are "Tower" and "Chute"?

In Sudoku, a Tower refers to three horizontally or vertically arranged boxes:

  • Horizontal Tower: Box 1-2-3 (Rows 1-3), Box 4-5-6 (Rows 4-6), Box 7-8-9 (Rows 7-9)
  • Vertical Tower: Box 1-4-7 (Columns 1-3), Box 2-5-8 (Columns 4-6), Box 3-6-9 (Columns 7-9)

Chute specifically refers to the 3 cells in a row (or column) within a box that runs parallel to the tower direction. For example, in a vertical tower, the 3 cells in column 4 of Box 2 form a Chute.

Example Analysis: Chute Remote Pairs in Vertical Tower

Let's look at an example where we find Chute Remote Pairs in the vertical tower (Box 2-5-8).

Sudoku Chute Remote Pairs Example - Vertical Tower
Fig. 1: In vertical tower (Box 2-5-8), R4C6 and R8C5 are both {3,6} pairs, Column 4 of Box 2 (Chute) has no 3
Open this example in calculator

Puzzle Data

First, let's look at the candidates in the cells of the vertical tower (Box 2-5-8, i.e., Columns 4-6):

Box 2 (Rows 1-3, Columns 4-6):

  • R1C4 = 6 (confirmed)
  • R1C5 = {3,5,7}
  • R1C6 = {3,7}
  • R2C4 = 2 (confirmed)
  • R2C5 = 8 (confirmed)
  • R2C6 = 1 (confirmed)
  • R3C4 = {4,5,9}
  • R3C5 = {4,5,7,9}
  • R3C6 = {7,9}

Box 5 (Rows 4-6, Columns 4-6):

  • R4C4 = {1,3,4,5}
  • R4C5 = {3,4,5,6}
  • R4C6 = {3,6}
  • R5C4 = {1,3,4,9}
  • R5C5 = {3,4,6,7,9}
  • R5C6 = {2,3,6,7,9}
  • R6C4 = {1,5,8,9}
  • R6C5 = {5,9}
  • R6C6 = {2,8,9}

Box 8 (Rows 7-9, Columns 4-6):

  • R7C4 = 7 (confirmed)
  • R7C5 = 2 (confirmed)
  • R7C6 = 5 (confirmed)
  • R8C4 = {3,8}
  • R8C5 = {3,6}
  • R8C6 = 4 (confirmed)
  • R9C4 = {3,8,9}
  • R9C5 = 1 (confirmed)
  • R9C6 = {3,6,8,9}

Analysis Process

1 Find pair cells: In the vertical tower (Box 2, 5, 8), we find that R4C6 (Box 5) and R8C5 (Box 8) are both the pair {3,6}.
2 Confirm position relationship: R4C6 is in Column 6, R8C5 is in Column 5, they are not in the same column (this is the key condition).
3 Determine Chute: The two pair cells are in Column 5 and Column 6, so Column 4 (the column where neither pair cell is) in the third box (Box 2) is the Chute, containing R1C4, R2C4, R3C4.
4 Check Chute: The cells in Column 4 of Box 2 (Chute) are:
  • R1C4 = 6 (confirmed)
  • R2C4 = 2 (confirmed)
  • R3C4 = {4,5,9}
The Chute has no candidate 3 (only 6, 2, 4, 5, 9)!
5 Reasoning process:
  • Since the Chute has no 3, the number 3 in Box 2 must be in Column 5 or Column 6
  • If Box 2's 3 is in Column 5 → R8C5 cannot be 3 (only one 3 per column) → R8C5 must be 6
  • If Box 2's 3 is in Column 6 → R4C6 cannot be 3 (only one 3 per column) → R4C6 must be 6
  • In either case, one of R4C6 and R8C5 must be 6
6 Find elimination targets: Cells that can see both R4C6 and R8C5 (within their row/column/box visibility):
  • R4C5 = {3,4,5,6}: Same row as R4C6, same column as R8C5 → contains 6, can eliminate
  • R5C5 = {3,4,6,7,9}: Same box as R4C6 (Box 5), same column as R8C5 → contains 6, can eliminate
  • R6C5 = {5,9}: Same box as R4C6 (Box 5), same column as R8C5 → doesn't contain 6, no action needed
  • R9C6 = {3,6,8,9}: Same column as R4C6 (Column 6), same box as R8C5 (Box 8) → contains 6, can eliminate
Conclusion:
The Chute (Box 2 Column 4) has no 3, meaning one of R4C6 and R8C5 must be 6.
Action: Eliminate candidate 6 from R4C5, R5C5, R9C6.

Key Point: Missing Number in Chute ≠ Number to Eliminate

Important Understanding:
A confusing aspect of this technique is that the candidate missing from the Chute and the candidate to eliminate are opposite!
  • Chute has no 3 → one of the pair cells must be 6 → eliminate 6
  • Chute has no 6 → one of the pair cells must be 3 → eliminate 3
This is because: Chute missing a number → that number must be in the row/column of the pair cells → excludes that number from the pair cells → pair cell can only be the other number.

How to Find Chute Remote Pairs?

Finding Chute Remote Pairs requires a systematic approach:

1 Find pair cells: First find all cells with only two candidates (pair cells).
2 Search for matching pairs: In the three boxes of the same tower, find two pair cells with identical candidates that are in different boxes.
3 Check position: Confirm that the two pair cells are not in the same row (horizontal tower) or not in the same column (vertical tower).
4 Determine Chute: Find the 3 cells in the third box in the row (or column) where neither pair cell is.
5 Check Chute: See if the Chute is missing one of the pair's candidates. If so, elimination can be performed.
6 Execute elimination: Eliminate the other candidate from positions that can see both pair cells.

What Does "Can See Both Pair Cells" Mean?

A cell can "see" another cell if they are in the same row, column, or box. To see both pair cells, one of the following conditions must be met:

  • Same row as Pair①, same column (or box) as Pair②
  • Same column as Pair①, same row (or box) as Pair②
  • Same box as Pair①, same row/column/box as Pair②

In this example:

  • R4C5 is in the same row (Row 4) as R4C6 and the same column (Column 5) as R8C5
  • R5C5 is in the same box (Box 5) as R4C6 and the same column (Column 5) as R8C5
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 both confirmed numbers and candidates
  • If the Chute is missing both candidates, the technique is not applicable (cannot determine which pair is which value)

Technique Summary

Key points for applying the Chute Remote Pairs method:

  • Recognition condition: Two boxes in the same tower each have a cell with the same pair, not in the same row/column
  • Key position: The row/column in the third box where neither pair cell is (Chute)
  • 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 positions that can see both pair cells
Practice Now:
Start a Sudoku game and try using the Chute Remote Pairs method for elimination! When you find two identical pair cells in different boxes of the same tower, remember to check the third box's Chute.
Pair Method Skyscraper Technique Index