Introduction
Obvious pairs is a fundamental Sudoku technique that identifies when two cells in the same region contain exactly the same two candidates. These two numbers must occupy those two cells, allowing elimination of those candidates from all other cells in that region. Learning obvious pairs significantly improves your ability to solve puzzles in Sudoku, making it an essential skill for progressing beyond basic elimination methods.
Obvious pairs are called "obvious" because the pattern is immediately visible with proper candidate notation—unlike hidden pairs which require careful analysis. This visibility makes obvious pairs easier to spot and apply, providing powerful eliminations that simplify puzzles and enable continued solving.
What Is Obvious Pairs Technique
Obvious pairs is a Sudoku solving technique that identifies when two cells in the same region (row, column, or box) contain exactly the same two candidates with no other possibilities. These two numbers must occupy those two cells, eliminating them from all other cells in that region. The technique is called "obvious" because the pattern is immediately visible with candidate notation.
Obvious pairs provide powerful eliminations that simplify puzzles significantly. When you identify an obvious pair, you can eliminate those two candidates from all other cells in that region, often revealing single candidates or creating conditions for other techniques. This technique is fundamental for intermediate solving.
Key Points
Point 1: Obvious Pairs Require Two Cells with Same Two Candidates
For an obvious pair to exist, two cells in the same region must contain exactly the same two candidates with no other possibilities. These cells obviously share the same candidate set, making the pattern immediately visible. The obvious nature makes this technique easier to spot than hidden pairs.
Point 2: Two Numbers Must Occupy Two Cells
When two cells contain the same two candidates, those two numbers must occupy those two cells. This logical necessity eliminates those two candidates from all other cells in that region. The elimination is based on mathematical certainty, not guessing.
Point 3: Obvious Pairs Work in All Regions
The technique applies to rows, columns, and boxes equally. Scan each region systematically to find two cells with identical candidate sets. The same logical principle works regardless of region type, making obvious pairs a versatile solving tool.
Point 4: Candidate Notation Makes Pattern Visible
Proper candidate notation makes obvious pairs immediately visible. Without notation, identifying two cells with the same two candidates is difficult. Complete notation enables quick pattern recognition and application.
Point 5: Obvious Pairs Often Reveal Other Patterns
After applying obvious pair eliminations, new patterns frequently emerge. Removing candidates may create naked singles, reveal other obvious pairs, or create conditions for advanced techniques. Obvious pairs often act as stepping stones to further progress.
How It Works (Step-by-Step)
Step 1: Scan Regions for Candidate Sets
Systematically scan each region (row, column, or box) looking for two cells that contain exactly the same two candidates. With proper candidate notation, these patterns are immediately visible. Scan methodically to ensure comprehensive coverage.
Step 2: Verify the Obvious Pair
When you find two cells with the same two candidates, verify they're in the same region and contain no other possibilities. Confirm the pattern is valid before applying eliminations. Verification ensures accurate solving.
Step 3: Eliminate Candidates from Other Cells
Once confirmed, eliminate those two candidates from all other cells in that region. The logic is that those two numbers must occupy those two cells, making them impossible elsewhere. This elimination simplifies the puzzle significantly.
Step 4: Update Candidate Notation
After making eliminations, update candidate notation in affected cells. Removing candidates may reveal naked singles or create other patterns. Regular updates maintain notation accuracy and enable continued solving.
Step 5: Continue Solving Systematically
After applying obvious pair eliminations, continue solving using other techniques. Obvious pair eliminations often create cascading solving opportunities. Continue the solving process with your updated information.
Examples
Example 1: Obvious Pair in a Box
In box 5, cells R4C5 and R6C5 both contain only candidates 3 and 7. This is an obvious pair, meaning 3 and 7 must occupy these two cells. Therefore, eliminate 3 and 7 from all other cells in box 5. This elimination reveals that R5C6 must be 2, creating further progress.
Example 2: Obvious Pair in a Row
In row 7, cells R7C2 and R7C8 both contain only candidates 4 and 9. This forms an obvious pair. Eliminate 4 and 9 from all other cells in row 7. This elimination may reveal naked singles or create other solving opportunities.
Example 3: Obvious Pair Revealing Naked Single
After applying an obvious pair elimination that removes candidates 2 and 5 from several cells in a column, a naked single appears. Cell R3C7, which previously had candidates 2, 3, 5, and 8, now cannot contain 2 or 5. With 3 and 8 also eliminated by other constraints, R3C7 becomes a naked single and must be 1.
Summary
Obvious pairs is a fundamental Sudoku technique that uses two-cell patterns to create logical eliminations. By recognizing when two cells contain the same two candidates, you can eliminate those candidates from other cells and simplify puzzles significantly. This technique is crucial for solving easy to medium puzzles where basic methods need extension.
Systematic scanning for obvious pairs improves solving efficiency and enables puzzle completion. Learning to recognize these patterns quickly is fundamental to intermediate Sudoku solving. This technique works alongside hidden pairs to provide comprehensive solving coverage.
Practice obvious pairs in Sudoku, then explore more in Sudoku Hidden Pairs Technique: Examples and Guide and Intermediate Sudoku Techniques: Boost Solving Skills. For different puzzles, try Number Puzzle or Word Puzzle.
FAQ (Frequently Asked Questions)
Q1: How do I distinguish obvious pairs from hidden pairs?
Obvious pairs are immediately visible—two cells contain exactly the same two candidates with no other possibilities. Hidden pairs are "hidden" because the cells contain additional candidates, but two numbers are restricted to just those two cells. Obvious pairs are easier to spot than hidden pairs.
Q2: Do I need candidate notation for obvious pairs?
Yes, candidate notation is essential for obvious pairs. Without seeing all possible candidates in cells, identifying two cells with the same two candidates is difficult. Proper notation makes obvious pairs immediately visible and easy to spot.
Q3: How often do obvious pairs appear in puzzles?
Obvious pairs appear regularly in easy to medium difficulty puzzles. In easy puzzles, you might find several obvious pairs. In medium puzzles, obvious pairs appear frequently and are essential for efficient solving. They're fundamental techniques for all difficulty levels.
Q4: Should I look for obvious pairs before or after other techniques?
Look for obvious pairs after basic techniques like single candidates and elimination, but before advanced techniques. Obvious pairs are intermediate techniques that bridge basic and advanced methods. They're often necessary for solving medium puzzles.
Q5: Can obvious pairs work with more than two cells?
The technique specifically requires two cells and two candidates. However, the same principle extends to obvious triples (three cells with three candidates), though these are less common. Obvious pairs provide the most common and useful pattern beyond singles.
Q6: What if I find an obvious pair but it doesn't help?
If an obvious pair doesn't immediately reveal new opportunities, continue solving with other techniques. The elimination still simplifies the puzzle and may help later. Sometimes obvious pairs create conditions for other techniques that aren't immediately obvious.
Next Steps
Ready to master obvious pairs? Play Sudoku now and practice identifying obvious pair patterns in puzzles. For more techniques, read Sudoku Hidden Pairs Technique: Examples and Guide and Intermediate Sudoku Techniques: Boost Solving Skills. Explore other puzzles in Number Puzzle and Word Puzzle.