Introduction
Obvious triples is an intermediate Sudoku technique that extends obvious pairs logic to three cells. When three cells in the same region contain exactly the same three candidates, those three numbers must occupy those cells, allowing elimination of those candidates from all other cells in that region. Learning obvious triples significantly improves your ability to solve medium to hard puzzles in Sudoku, making it an essential skill for progressing beyond basic methods.
Obvious triples are called "obvious" because the pattern is immediately visible with proper candidate notation—unlike hidden triples which require careful analysis. This visibility makes obvious triples easier to spot and apply, providing powerful eliminations that simplify puzzles.
What Is Obvious Triples Technique
Obvious triples is a Sudoku solving technique that identifies when three cells in the same region (row, column, or box) contain exactly the same three candidates with no other possibilities. These three numbers must occupy those three 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 triples extend obvious pairs logic to three dimensions, providing more powerful eliminations. Three-cell patterns create logical necessities that enable eliminations not possible with two-cell patterns. This extension is essential for solving medium to hard puzzles efficiently.
Key Points
Point 1: Obvious Triples Require Three Cells with Same Three Candidates
For an obvious triple to exist, three cells in the same region must contain exactly the same three 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 triples.
Point 2: Three Numbers Must Occupy Three Cells
When three cells contain the same three candidates, those three numbers must occupy those three cells. This logical necessity eliminates those three candidates from all other cells in that region. The elimination is based on mathematical certainty, not guessing.
Point 3: Obvious Triples Work in All Regions
The technique applies to rows, columns, and boxes equally. Scan each region systematically to find three cells with identical candidate sets. The same logical principle works regardless of region type, making obvious triples a versatile solving tool.
Point 4: Candidate Notation Makes Pattern Visible
Proper candidate notation makes obvious triples immediately visible. Without notation, identifying three cells with the same three candidates is difficult. Complete notation enables quick pattern recognition and application.
Point 5: Obvious Triples Often Reveal Other Patterns
After applying obvious triple eliminations, new patterns frequently emerge. Removing candidates may create naked singles, reveal other obvious patterns, or create conditions for advanced techniques. Obvious triples 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 three cells that contain exactly the same three candidates. With proper candidate notation, these patterns are immediately visible. Scan methodically to ensure comprehensive coverage.
Step 2: Verify the Obvious Triple
When you find three cells with the same three 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 three candidates from all other cells in that region. The logic is that those three numbers must occupy those three 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 triple eliminations, continue solving using other techniques. Obvious triple eliminations often create cascading solving opportunities. Continue the solving process with your updated information.
Examples
Example 1: Obvious Triple in a Box
In box 5, cells R4C5, R5C5, and R6C5 all contain only candidates 2, 5, and 8. This is an obvious triple, meaning 2, 5, and 8 must occupy these three cells. Therefore, eliminate 2, 5, and 8 from all other cells in box 5. This elimination reveals that R5C6 must be 3, creating further progress.
Example 2: Obvious Triple in a Row
In row 7, cells R7C2, R7C5, and R7C8 all contain only candidates 3, 6, and 9. This forms an obvious triple. Eliminate 3, 6, and 9 from all other cells in row 7. This elimination may reveal naked singles or create other solving opportunities.
Example 3: Obvious Triple Revealing Naked Single
After applying an obvious triple elimination that removes candidates 1, 4, and 7 from several cells in a column, a naked single appears. Cell R3C7, which previously had candidates 1, 2, 4, 5, and 7, now cannot contain 1, 4, or 7. With 2 and 5 also eliminated by other constraints, R3C7 becomes a naked single and must be 3.
Summary
Obvious triples is an essential intermediate Sudoku technique that uses three-cell patterns to create logical eliminations. By recognizing when three cells contain the same three candidates, you can eliminate those candidates from other cells and simplify puzzles significantly. This technique is crucial for solving medium to hard puzzles where basic methods are insufficient.
Systematic scanning for obvious triples improves solving efficiency and enables puzzle completion. Learning to recognize these patterns quickly is fundamental to intermediate Sudoku solving. This technique works alongside obvious pairs to provide comprehensive solving coverage.
Practice obvious triples in Sudoku, then explore more in Sudoku Hidden Triples 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 triples from hidden triples?
Obvious triples are immediately visible—three cells contain exactly the same three candidates with no other possibilities. Hidden triples are "hidden" because the cells contain additional candidates, but three numbers are restricted to just those three cells. Obvious triples are easier to spot than hidden triples.
Q2: Do I need candidate notation for obvious triples?
Yes, candidate notation is essential for obvious triples. Without seeing all possible candidates in cells, identifying three cells with the same three candidates is difficult. Proper notation makes obvious triples immediately visible and easy to spot.
Q3: How often do obvious triples appear in puzzles?
Obvious triples appear regularly in medium to hard difficulty puzzles. In medium puzzles, you might find one or two obvious triples. In hard puzzles, obvious triples appear more frequently. They're essential for efficient medium puzzle solving.
Q4: Should I look for obvious triples before or after other techniques?
Look for obvious triples after basic techniques like single candidates and elimination, but before advanced techniques. Obvious triples are intermediate techniques that bridge basic and advanced methods. They're often necessary for solving medium puzzles.
Q5: Can obvious triples work with more than three cells?
The technique specifically requires three cells and three candidates. However, the same principle extends to obvious quads (four cells with four candidates), though these are less common. Obvious triples provide the most common and useful extension beyond pairs.
Q6: What if I find an obvious triple but it doesn't help?
If an obvious triple doesn't immediately reveal new opportunities, continue solving with other techniques. The elimination still simplifies the puzzle and may help later. Sometimes obvious triples create conditions for other techniques that aren't immediately obvious.
Next Steps
Ready to master obvious triples? Play Sudoku now and practice identifying obvious triple patterns in medium difficulty puzzles. For more techniques, read Sudoku Hidden Triples Technique: Examples and Guide and Intermediate Sudoku Techniques: Boost Solving Skills. Explore other puzzles in Number Puzzle and Word Puzzle.