Reduksi Box-Line Sudoku: Menggunakan Persimpangan Kotak dan Garis

Box-Line Reduction (also called Pointing & Claiming) is a very practical method among intermediate Sudoku techniques. This technique uses the intersection relationships between boxes (3×3 regions) and rows/columns to eliminate candidates, and is divided into two types: Pointing and Claiming.

Before reading this article, we recommend understanding the Sudoku naming conventions for rows, columns, and boxes, which will help you understand the analysis examples below.

Type 1: Pointing

Pointing means: when a candidate appears in a box only in the same row or column, that candidate can be eliminated from the other boxes in that row/column.

Let's look at an example:

Figure 1: Candidate 3 in Box 8 only appears in Row 8, so candidate 3 can be removed from Box 9 in Row 8

Current Board Data

Based on the CSV81 format candidate data, we focus on Box 8 (R7-R9, C4-C6) and Row 8:

Cells in Box 8:

• R7C4: Filled with 7
• R7C5: Filled with 9
• R7C6: Filled with 6
• R8C4: Filled with 5
• R8C5: Candidates {1, 2, 3, 4}
• R8C6: Candidates {1, 2, 3, 4}
• R9C4: Candidates {1, 2}
• R9C5: Filled with 8
• R9C6: Candidates {1, 2}

Row 8 cells in Box 9 (R8C7-R8C9):

• R8C7: Candidates {3, 6, 8, 9}
• R8C8: Candidates {1, 2, 3, 6, 9}
• R8C9: Candidates {1, 2, 3, 9}

Analysis Process

Type 2: Claiming

Claiming is the reverse application of Pointing: when a candidate appears in a row or column only within one box, that candidate can be eliminated from the other rows/columns of that box.

Let's look at another example:

Figure 2: Candidate 4 in Column 4 only appears in Box 5, so candidate 4 can be removed from other columns in Box 5

Current Board Data

Based on the CSV81 format candidate data, we focus on Column 4 and Box 5 (R4-R6, C4-C6):

Column 4 cells:

• R1C4: Filled with 8
• R2C4: Filled with 6
• R3C4: Filled with 3
• R4C4: Candidates {1, 2, 4, 9}
• R5C4: Candidates {4, 9}
• R6C4: Candidates {2, 4, 9}
• R7C4: Filled with 7
• R8C4: Filled with 5
• R9C4: Candidates {1, 2}

Box 5 cells to check:

• R4C5: Candidates {1, 2, 3, 4}
• R4C6: Filled with 8
• R5C5: Filled with 6
• R5C6: Filled with 7
• R6C5: Filled with 5
• R6C6: Candidates {2, 3, 4}

Analysis Process

Pointing vs Claiming Comparison

These two types are essentially the same principle from different perspectives:

Practical Application Steps

When solving, follow these steps to find Box-Line Reduction opportunities:

1. Mark candidates: Make sure you have marked all candidates in all cells
2. Check each box: Check box by box whether candidates are concentrated in the same row or column
3. Check each row and column: Check row by row and column by column whether candidates are concentrated in the same box
4. Execute elimination: When you find a qualifying condition, immediately delete the candidates
5. Chain reaction: After elimination, new Naked Single or elimination opportunities may arise, continue solving

Technique Summary

Key points of Box-Line Reduction:

• Use intersections: Cleverly use the intersection relationships between boxes and rows/columns for elimination
• Bidirectional observation: Look at rows/columns from the box perspective, and look at boxes from the row/column perspective
• Concentration principle: Candidates must be "concentrated" in the intersection area to apply this technique
• Immediate elimination: Execute immediately when you find an opportunity, don't accumulate too many steps

Practice Suggestions

To skillfully apply Box-Line Reduction, we recommend:

• When solving, systematically check the relationship between each box and rows/columns, don't skip by intuition
• Use different colors to mark candidates, helping visually identify concentrated areas
• For medium difficulty puzzles, first use beginner techniques, then actively look for Box-Line Reduction opportunities
• Understanding the principle is more important than memorizing terms, understand "why you can eliminate"