Pointing Pairs Sudoku Technique
Pointing pairs (also called “locked candidates Type 1” or “pointing lines”) are one of the most useful intermediate Sudoku techniques. Once you’ve mastered naked singles and hidden singles, pointing pairs are typically the next technique you should learn. They’re relatively easy to spot and can eliminate candidates that no single or pair technique can touch.
Prerequisites
Before learning pointing pairs, you should be confident with:
- Candidate notation (pencil marks) — listing all possible numbers in each empty cell
- Naked singles and hidden singles — the foundational techniques
- Basic understanding of how rows, columns, and 3×3 boxes interact
What is a Pointing Pair?
A pointing pair occurs when a candidate number within a 3×3 box is restricted to only two cells, and those two cells are in the same row or same column. Because the candidate must be placed in one of those two cells (it has no other option within the box), it follows that the candidate cannot appear anywhere else in that row or column outside the box.
In other words, the box “points” the candidate along a row or column, and you can safely eliminate that candidate from all other cells in that line.
The Key Insight
The logic relies on the interaction between two Sudoku constraints:
- Box constraint: Every number must appear exactly once in each 3×3 box
- Row/column constraint: Every number must appear exactly once in each row and column
When a candidate is locked to one row (or column) within a box, the box constraint guarantees placement in that line, and the row/column constraint lets you eliminate it from the rest of the line.
How to Find Pointing Pairs: Step-by-Step
Step 1: Focus on One Box at a Time
Choose a 3×3 box and examine the pencil marks inside it. For each candidate number, note which cells contain it.
Step 2: Check Each Candidate for Alignment
For each candidate in the box, ask: Are all instances of this candidate in a single row or single column?
- If the candidate appears in cells that span multiple rows AND multiple columns within the box — no pointing pair exists for that candidate in that box.
- If the candidate appears in only one row (or one column) within the box — you’ve found a pointing pair (or pointing triple if there are three cells).
Step 3: Eliminate Along the Line
Remove the candidate from every cell in that row (or column) outside the box. The cells inside the box keep their candidates — you’re only eliminating from the rest of the line.
Worked Example 1: Row-Based Pointing Pair
Consider the top-left 3×3 box (Box 1). After filling in pencil marks:
| Col 1 | Col 2 | Col 3 | |
|---|---|---|---|
| Row 1 | 3, 7 | 5, 9 | 5, 8 |
| Row 2 | 1, 4 | 6 | 2, 9 |
| Row 3 | 2, 7 | 8, 4 | 1, 3 |
Look at the candidate 5 inside Box 1:
- 5 appears in Row 1, Col 2
- 5 appears in Row 1, Col 3
- 5 does NOT appear in Row 2 or Row 3 within this box
Since 5 is restricted to Row 1 within Box 1, it must be placed in Row 1 somewhere in columns 2 or 3. Therefore, 5 cannot appear in Row 1 outside of Box 1 — eliminate 5 from Row 1, Col 4 through Col 9.
Result: If any cells in Row 1, columns 4–9 had 5 as a candidate, remove it immediately.
Worked Example 2: Column-Based Pointing Pair
Now consider the center box (Box 5). After checking pencil marks:
| Col 4 | Col 5 | Col 6 | |
|---|---|---|---|
| Row 4 | 2, 9 | 1, 3 | 6, 7 |
| Row 5 | 8, 4 | 3, 5 | 2, 9 |
| Row 6 | 8, 1 | 7, 6 | 4, 5 |
Look at the candidate 8 inside Box 5:
- 8 appears in Row 5, Col 4
- 8 appears in Row 6, Col 4
- 8 does NOT appear in Col 5 or Col 6 within this box
Since 8 is locked to Col 4 within Box 5, eliminate 8 from all other cells in Col 4 outside the box — specifically from rows 1–3 and rows 7–9 in column 4.
Pointing Pair vs. Box-Line Reduction
These are closely related but work in opposite directions:
| Technique | Starting constraint | Elimination target |
|---|---|---|
| Pointing Pair | Candidate locked to one line within a box | Eliminate from the rest of that line |
| Box-Line Reduction | Candidate in a line restricted to one box | Eliminate from the rest of that box |
Both are classified as “locked candidates” and use the same underlying logic — the interaction between box and line constraints. Together they form a powerful pair of intermediate techniques.
Common Mistakes to Avoid
Eliminating from inside the box. Only eliminate from cells in the row/column that are outside the pointing pair’s box. The cells inside the box keep their candidates.
Missing column-based patterns. Many solvers habitually scan rows but forget to check columns. Always look both ways.
Confusing with hidden pairs. A hidden pair involves two candidates restricted to two cells within a unit. A pointing pair involves one candidate restricted to one line within a box. Different technique entirely.
Incomplete pencil marks. Pointing pairs are invisible without accurate candidate notation. If your pencil marks are wrong, you might eliminate a candidate that shouldn’t be eliminated — leading to an unsolvable puzzle.
Tips for Spotting Pointing Pairs Quickly
- Scan box by box rather than scanning the whole grid at once. Focus on one box, check all candidates, then move to the next box.
- Start with digits that are mostly solved. If 6 of the nine 4s are already placed, the remaining 4s have very limited positions — making pointing pairs easier to spot.
- Use pencil marks consistently. Pointing pairs are almost impossible to find without written candidates.
- Look for pointing pairs immediately after placing a digit. When you fill in a cell, it often restricts candidates in the neighboring box, creating new pointing pair opportunities.
When to Use Pointing Pairs
Pointing pairs sit at the intermediate level in the solving hierarchy. Use them after exhausting:
- Naked singles and hidden singles
- Direct elimination from given clues
And before moving to:
- Naked pairs and hidden pairs
- Pointing triples (same logic, three cells)
- Advanced techniques like X-Wings or Swordfish
Many Medium and Hard puzzles require pointing pairs. You’ll use them constantly — they’re one of the most frequently needed techniques beyond basic singles.
Frequently Asked Questions
What’s the difference between a pointing pair and a pointing triple?
A pointing pair has exactly two cells containing the candidate (both aligned in one line within a box). A pointing triple has three cells — all three are in the same row or column within the box. The elimination logic is identical: remove the candidate from the rest of that row/column outside the box.
Can pointing pairs solve a whole puzzle?
No, but they’re frequently the key that unlocks further progress. After a pointing pair elimination, new naked singles or hidden singles often appear, cascading through the puzzle.
How common are pointing pairs?
Very common. Most Medium and Hard puzzles contain multiple pointing pair opportunities. They’re one of the most frequently used intermediate techniques.
Do I need to know pointing pairs for easy puzzles?
Typically not — Easy puzzles are designed to be solvable with naked and hidden singles alone. But knowing pointing pairs makes you significantly faster even on easier puzzles.
Practice Pointing Pairs
Ready to put this technique into practice? Try our Medium or Hard difficulty puzzles — these frequently require pointing pairs to solve.
Practice Pointing Pairs Sudoku Technique
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