Pointing Pair Technique
Quick Summary
A Pointing Pair occurs when all possible positions for a specific digit within a 3×3 box are confined to a single row or column. This allows you to eliminate that digit from other cells in the same row or column outside of that box.
What is a Pointing Pair?
A Pointing Pair is an intermediate Sudoku technique that involves identifying when all possible positions for a specific digit within a 3×3 box are confined to a single row or column. This creates a "pointing" effect where the digit "points" to that row or column.
The key insight is that if a digit can only go in cells that are all in the same row or column within a box, then that digit cannot appear anywhere else in that row or column outside of the box.
Why is it Called "Pointing Pair"?
The term "pointing" refers to the fact that the digit "points" to a specific row or column. When all possible positions for a digit in a box are aligned in the same row or column, it's as if the digit is pointing to that row or column.
The term "pair" refers to the fact that this technique typically involves two cells (though it can involve more), and these cells form a "pair" that points to the same row or column.
How to Find Pointing Pairs
Follow these steps to identify pointing pairs:
- 1Choose a 3×3 box to analyze
- 2Pick a digit (1-9) to focus on
- 3Find all cells in that box where the digit could go
- 4Check alignment: Are all possible cells in the same row or column?
- 5Apply elimination: Remove that digit from other cells in the same row/column outside the box
Step-by-Step Example
Let's work through a detailed example. In the puzzle below, we'll look for a pointing pair in the highlighted box:
Step 1: Analyze the Box
The top-left box currently contains: 5, 3, 6, 9, 8
Missing digits: 1, 2, 4, 7
Empty cells: R1C3, R1C4, R2C2, R2C3, R3C1, R3C4, R3C5, R3C6, R3C7
Step 2: Check Each Missing Digit
Let's check where each missing digit can go in this box:
- • Digit 1: Can go in R1C3, R1C4, R2C2, R2C3, R3C1, R3C4, R3C5, R3C6, R3C7
- • Digit 2: Can go in R1C3, R1C4, R2C2, R2C3, R3C1, R3C4, R3C5, R3C6, R3C7
- • Digit 4: Can go in R1C3, R1C4, R2C2, R2C3, R3C1, R3C4, R3C5, R3C6, R3C7
- • Digit 7: Can go in R1C3, R1C4, R2C2, R2C3, R3C1, R3C4, R3C5, R3C6, R3C7
Step 3: Look for Alignment
Let me check if any digit is confined to a single row or column:
- • Digit 1 in Row 1: Can go in R1C3, R1C4 (both in the same row)
- • Digit 1 in Row 2: Can go in R2C2, R2C3 (both in the same row)
- • Digit 1 in Row 3: Can go in R3C1, R3C4, R3C5, R3C6, R3C7 (spread across multiple columns)
I see! Digit 1 in Row 1 is confined to columns 3 and 4, and digit 1 in Row 2 is confined to columns 2 and 3. Let me check if this creates a pointing pair...
Step 4: Detailed Analysis
Let me check the constraints more carefully for digit 1:
- • R1C3: Check row 1 (5,3), column 3 (1,8), box (5,3,6,9,8) - 1 is possible
- • R1C4: Check row 1 (5,3), column 4 (7,9,6,2,1,8), box (5,3,6,9,8) - 1 is possible
- • R2C2: Check row 2 (6,1,9,5), column 2 (3,9), box (5,3,6,9,8) - 1 is possible
- • R2C3: Check row 2 (6,1,9,5), column 3 (1,8), box (5,3,6,9,8) - 1 is possible
Actually, let me check if there's a digit that's more constrained. Let me look at digit 3...
Step 5: Re-examine the Constraints
Let me check the constraints more carefully:
- • R1C3: Row 1 has 5,3. Column 3 has 1,8. Box has 5,3,6,9,8. Missing: 2,4,6,7,9
- • R1C4: Row 1 has 5,3. Column 4 has 7,9,6,2,1,8. Box has 5,3,6,9,8. Missing: 4
- • R2C2: Row 2 has 6,1,9,5. Column 2 has 3,9. Box has 5,3,6,9,8. Missing: 2,4,7
- • R2C3: Row 2 has 6,1,9,5. Column 3 has 1,8. Box has 5,3,6,9,8. Missing: 2,4,7
I see! R1C4 can only contain 4, and R2C2 and R2C3 can both contain 2,4,7. This means digit 4 in Row 1 is confined to column 4, and digits 2,4,7 in Row 2 are confined to columns 2 and 3. This creates a pointing pair for digit 4!
Practice Exercise
Try finding pointing pairs in this practice puzzle:
Tips for Finding Pointing Pairs
1. Focus on Boxes First
Start by analyzing each 3×3 box systematically. Look for digits that are confined to a single row or column within that box.
2. Check Alignment Carefully
Make sure all possible positions for a digit in a box are aligned in the same row or column. If they're spread across multiple rows or columns, it's not a pointing pair.
3. Use Pencil Marks
Keep detailed pencil marks showing all possible candidates in each cell. This makes it much easier to spot when digits are confined to specific rows or columns.
4. Look for Patterns
Pointing pairs often appear in boxes that are nearly complete or have many constraints. Look for boxes with 6 or 7 filled cells.
Why Pointing Pairs Work
Pointing Pairs work because of the fundamental Sudoku rules:
- •Each row must contain all digits 1-9 exactly once
- •Each column must contain all digits 1-9 exactly once
- •Each 3×3 box must contain all digits 1-9 exactly once
If a digit can only go in cells that are all in the same row or column within a box, then that digit must appear in that row or column. This means it cannot appear anywhere else in that row or column outside of the box.
When to Use Pointing Pairs
Pointing Pairs should be used:
- •After applying basic techniques (Last Free Cell, Naked Single, Hidden Single, Naked Pair)
- •When you have good pencil marks showing possible candidates
- •As a stepping stone to more advanced techniques
- •When you get stuck and need to look for logical moves
Common Mistakes to Avoid
- •Wrong alignment: Make sure all possible positions are in the same row or column
- •Incomplete analysis: Check all possible positions for the digit in the box
- •Wrong elimination: Only eliminate from the same row/column outside the box
- •Rushing: Take time to verify the alignment and constraints
Next Steps
Once you've mastered Pointing Pairs, you're ready to learn about Box/Line Reduction, which is the inverse of Pointing Pair. Box/Line Reduction involves finding when all possible positions for a digit in a row or column are within the same box.
Ready for the Next Technique?
Practice your Pointing Pair skills or learn the next technique in the sequence.