Box/Line Reduction
Eliminate candidates from boxes when all occurrences of a number in a row or column are confined to a single box.
What Is Box/Line Reduction?
Box/Line Reduction (also called "Claiming") is the reverse of Pointing Pairs. It occurs when all the possible positions for a specific number within a row or column are contained entirely within one 3x3 box.
Key Insight
If a number in a row or column can only appear within one box, then that number must be in that box's portion of the line. Therefore, we can eliminate it from other cells in the same box that aren't in that line.
How Box/Line Reduction Works
The Process
- 1 Examine a row or column for a specific candidate
- 2 Check if all occurrences are within one 3x3 box
- 3 Eliminate that candidate from other rows/columns within that box
Pointing vs Box/Line
These are complementary techniques:
- Pointing Pairs: Look at BOX, eliminate from LINE
- Box/Line Reduction: Look at LINE, eliminate from BOX
The line "claims" that portion of the box for itself!
Example: Row Claims a Box
In this example, looking at Row 4, the number 6 can only appear within the center box:
Blue cells: The only places 6 can go in Row 4 (all in center box)
The Elimination
Since 6 must be in the center box's Row 4 cells, we can eliminate 6 from other cells in the center box (Row 5 and Row 6):
Before
Other cells in center box might have 6 as candidate
After
6 eliminated from Row 5 and Row 6 within the center box
Result
Row 4 "claims" the 6 for itself within the center box. No other row in that box can contain 6.
When to Use Box/Line Reduction
Best Scenarios
- ✓ Rows/columns with limited candidate positions
- ✓ When singles and pairs don't reveal progress
- ✓ Medium to hard puzzles
- ✓ Combined with Pointing Pairs for maximum effect
Common Mistakes
- ✗ Confusing with Pointing Pairs direction
- ✗ Eliminating from the wrong area
- ✗ Not checking all rows and columns
- ✗ Missing the technique when it applies
Practice Tips
How to Find Box/Line Reductions
- 1 For each row/column, track where each number can go
- 2 Look for numbers confined to one box
- 3 Eliminate from other rows/columns in that box
Related Techniques
- Pointing Pairs - The complementary technique
- X-Wing - Advanced pattern elimination
- Y-Wing - Chain-based elimination
Ready to Practice Box/Line Reduction?
Look for rows and columns where candidates are confined to a single box!
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