Pointing Pairs & Triples in Sudoku: The Complete Guide
What is a Pointing Pair?
A pointing pair occurs when a candidate number appears in only two cells within a box, and those cells are aligned in the same row or column. This "points" to that row or column, allowing you to eliminate that candidate from other cells in the same row or column outside the box.
A pointing triple works the same way but involves three cells instead of two.
Example:
In Box 1 (top-left), the number 7 appears as a candidate in only two cells: row 1, column 2 and row 1, column 3. Since 7 is locked to row 1 within this box, it must go somewhere in row 1 of Box 1. Therefore, you can eliminate 7 from all other cells in row 1 (in boxes 2 and 3).
Why Pointing Pairs Matter
- They create powerful eliminations across box boundaries.
- They work when simpler techniques like naked singles fail.
- They often trigger chain reactions, revealing hidden singles.
- They're essential for intermediate and advanced puzzles.
- They're also called "Locked Candidates Type 1" in Sudoku literature.
How to Spot a Pointing Pair or Triple
- Focus on one box at a time.
Pick any of the nine 3×3 boxes on the grid. - Check each candidate number (1-9).
For each number, identify which cells in that box contain it as a candidate. - Look for alignment in a row or column.
If a candidate appears in only 2 or 3 cells and they're all in the same row or column, you've found a pointing pair or triple. - Eliminate from the pointing line.
Remove that candidate from all other cells in the same row or column, but only outside the box.
Pointing Pairs vs Box-Line Reduction
These are complementary techniques, both dealing with "locked candidates":
- Pointing Pair/Triple (Locked Candidates Type 1): Start with a box. When candidates in a box are confined to one row or column, eliminate from that row/column outside the box.
- Box-Line Reduction (Locked Candidates Type 2): Start with a row or column. When candidates in a row/column are confined to one box, eliminate from that box outside the row/column.
Think of it this way: pointing pairs point outward from the box, while box-line reduction draws inward to the box.
Step-by-Step Example
Let's examine Box 4 (middle-left box):
Box 4 cells (rows 4-6, columns 1-3):
- Row 4, Col 1: {2, 6}
- Row 4, Col 2: {2, 4, 6}
- Row 4, Col 3: {2, 4}
- Row 5, Col 1: [filled with 8]
- Row 5, Col 2: {5, 7}
- Row 5, Col 3: {5, 7, 9}
- Row 6, Col 1: {1, 3}
- Row 6, Col 2: {1, 3, 5, 7}
- Row 6, Col 3: [filled with 9]
Analysis: Let's check where candidate 4 appears in Box 4:
- 4 appears in: Row 4, Col 2 and Row 4, Col 3
- Both cells are in Row 4
- This is a pointing pair!
Conclusion: Since 4 must be in Row 4 within Box 4, we can eliminate 4 from all other cells in Row 4 that are outside Box 4 (columns 4-9 of Row 4).
Result: Check Row 4 in boxes 5 and 6, and remove candidate 4 from any cells there.
Visual Example: Pointing Triple
- Scenario: In Box 7 (bottom-left), candidate 3 appears in three cells: all in column 2.
- Cells: (Row 7, Col 2), (Row 8, Col 2), (Row 9, Col 2)
- Observation: All three instances of candidate 3 in Box 7 are confined to column 2.
- Pointing triple identified: The number 3 "points" to column 2.
- Elimination: Remove candidate 3 from all other cells in column 2 outside Box 7 (rows 1-6 of column 2).
- Impact: This might reveal a hidden single for 3 elsewhere in column 2, or reduce candidates in rows 1-6.
Strategies for Spotting Pointing Pairs Quickly
- Systematic box scanning
Go through each of the 9 boxes methodically. For each box, check all candidates 1-9. - Look for sparse candidates
Numbers that appear in only 2-3 cells in a box are prime candidates for pointing pairs. - Visual column/row alignment
Train your eye to spot when candidates form a horizontal or vertical line within a box. - Use pencil marks consistently
Pointing pairs are much easier to spot when all candidates are clearly marked. - Check after each placement
Every time you fill a cell, new pointing pairs might emerge in affected boxes.
Common Pitfalls
- Eliminating from the wrong area: Only eliminate from the pointing row/column outside the box, never inside.
- Missing candidates: If you haven't marked all candidates, you might miss a third cell and think you have a pointing pair when you don't.
- Confusing with box-line reduction: Remember which direction you're working: box → line (pointing) or line → box (box-line reduction).
- Overlooking diagonal patterns: Pointing pairs/triples must be in the same row OR column, not diagonal.
- Forgetting to check all boxes: Don't just check one or two boxes—systematic scanning finds more opportunities.
Practice: Find the Pointing Pair
Try this Box 2 (top-middle) scenario:
Box 2 cells (rows 1-3, columns 4-6):
- Row 1, Col 4: {5, 8}
- Row 1, Col 5: [filled with 6]
- Row 1, Col 6: {3, 5, 8}
- Row 2, Col 4: {1, 7}
- Row 2, Col 5: {1, 7, 9}
- Row 2, Col 6: [filled with 2]
- Row 3, Col 4: [filled with 4]
- Row 3, Col 5: {1, 7, 9}
- Row 3, Col 6: {3, 5, 8}
Question: Can you find a pointing pair or triple?
Solution: Look at candidate 3 in Box 2:
- 3 appears in: Row 1, Col 6 and Row 3, Col 6
- Both are in column 6
- Pointing pair found! Candidate 3 points to column 6.
Action: Eliminate candidate 3 from all other cells in column 6 outside Box 2 (rows 4-9 of column 6).
Why Pointing Pairs Set the Stage
Pointing pairs introduce the concept of locked candidates—a fundamental principle in Sudoku solving. Once you understand this technique:
- You'll naturally progress to box-line reduction (the complementary technique)
- You'll start thinking about candidate distribution across multiple units
- You'll be prepared for advanced techniques like X-Wing and Swordfish, which use similar alignment principles
- You'll solve intermediate puzzles much faster by catching eliminations early
Quick Recap
| Technique | How it Works | Starting Point | Difficulty |
|---|---|---|---|
| Pointing Pair/Triple | Candidates in box confined to one row/col | Box → Line | Intermediate |
| Box-Line Reduction | Candidates in row/col confined to one box | Line → Box | Intermediate |
| Naked Pair | Two cells with same two candidates | Any unit | Intermediate |
| Hidden Pair | Two candidates appear in only two cells | Any unit | Intermediate |
Final Thought
When you're stuck, ask yourself: are any candidates locked to a single row or column within a box? Pointing pairs might be your breakthrough.
Frequently Asked Questions
What is a Pointing Pair in Sudoku?
A pointing pair occurs when a candidate number appears in only two cells within a box, and those cells are aligned in the same row or column. This "points" to that row or column, allowing you to eliminate that candidate from other cells in the same row or column outside the box. Also called Locked Candidates Type 1.
How do I spot a Pointing Pair or Pointing Triple?
To spot pointing pairs/triples: 1) Look at a single 3×3 box, 2) For each candidate number, check where it appears in that box, 3) If a candidate appears in only 2 or 3 cells and they're all in the same row or column, you've found a pointing pair or triple, 4) Eliminate that candidate from other cells in that row/column outside the box.
What's the difference between Pointing Pairs and Box-Line Reduction?
Pointing Pairs (Locked Candidates Type 1) start with a box: when candidates in a box are confined to one row/column, eliminate from that row/column outside the box. Box-Line Reduction (Locked Candidates Type 2) starts with a row/column: when candidates in a row/column are confined to one box, eliminate from that box outside the row/column. They're complementary techniques.
Why are Pointing Pairs important?
Pointing pairs are important because they create powerful eliminations across box boundaries, they work when simpler techniques fail, they often trigger chain reactions revealing hidden singles, and they're essential for intermediate and advanced puzzles.
When should I look for Pointing Pairs?
Look for pointing pairs after exhausting naked and hidden singles. They're especially effective when a box has few candidates for a particular number. Systematically check each box for each number 1-9, looking for candidates confined to a single row or column.
Ready to advance? Check out our complete strategy guide for more techniques.
Related Strategies
Once you've mastered pointing pairs, these techniques build naturally:
- Box-Line Reduction - The complementary locked candidates technique (coming soon)
- Hidden Singles - Often revealed after pointing pair eliminations
- Naked Pairs - Another intermediate elimination technique
- Hidden Pairs - Works within a single unit
- X-Wing - Advanced pattern using similar alignment principles
Practice Pointing Pairs
Next up: Try Box-Line Reduction to complete your locked candidates toolkit (coming soon).