Introduction

Obvious Triples (also called Naked Triples) is a powerful intermediate Sudoku technique that enables significant eliminations in medium to hard puzzles. Unlike Hidden Triples, which are subtle, Obvious Triples are visually apparent—three cells contain only three candidates total. This makes them easier to spot and apply. This guide provides everything you need to master this essential technique through clear explanations, step-by-step instructions, and detailed examples.

What Is the Obvious Triples Technique

Obvious Triples is an elimination technique that works when three cells in the same unit (row, column, or box) contain only three candidates total, in various combinations. For example, three cells might contain: cell 1 has candidates 2, 5, 8; cell 2 has candidates 2, 5; cell 3 has candidates 5, 8. Together, these three cells contain only candidates 2, 5, and 8.

The key insight is that these three cells must contain those three candidates (in some order). This means those three candidates cannot appear in any other cells in that unit, allowing elimination. The technique is called "obvious" because the pattern is visually apparent—you can see at a glance that three cells contain only three candidates.

Obvious Triples are particularly valuable in medium to hard puzzles where you have candidate notation and need to eliminate possibilities. They often appear after you've filled some cells and updated candidate notation, creating the specific conditions needed. Learning to spot Obvious Triples significantly improves your solving efficiency.

Key Points

1. Three Cells, Three Candidates: Obvious Triples require three cells containing only three candidates total (in various combinations).

2. Visually Obvious: Unlike Hidden Triples, the pattern is visually apparent—you can see the three cells contain only three candidates.

3. Forced Placement: The three candidates must occupy those three cells, enabling elimination from other cells in the unit.

4. Elimination Power: You can eliminate the three candidates from all other cells in that unit.

5. Candidate Notation Required: While obvious once found, Obvious Triples require candidate notation to identify.

How to Identify and Apply Obvious Triples

Step 1: Set Up Complete Candidate Notation

Obvious Triples identification requires complete candidate notation. Ensure every empty cell has all possible candidates marked. Incomplete notation will cause you to miss Obvious Triple opportunities.

Step 2: Scan Units for Triple Patterns

Scan each unit (row, column, box) looking for three cells that together contain only three candidates. Look for cells where the total number of unique candidates across the three cells is exactly three. The cells can have different combinations (one cell might have all three, another might have two, etc.), but together they must contain exactly three unique candidates.

Step 3: Verify the Pattern

Confirm that the three cells contain only three unique candidates total. Check that no other candidates appear in these three cells. If additional candidates are present, it's not a valid Obvious Triple. Verification ensures accurate identification.

Step 4: Apply Elimination

Once verified, eliminate the three candidates from all other cells in that unit. These eliminations are logically forced because the three candidates must occupy the three triple cells, leaving no room for them elsewhere in the unit.

Step 5: Update and Continue

After making eliminations, update your candidate notation throughout the puzzle. The new eliminations may reveal additional placements or create opportunities for other techniques. Continue scanning for more Obvious Triples or other solving opportunities.

Examples

Example 1: Obvious Triple in a Row

In row 6, cells R6C2, R6C5, and R6C8 contain: R6C2 has candidates 2, 5, 8; R6C5 has candidates 2, 5; R6C8 has candidates 5, 8. Together, these three cells contain only candidates 2, 5, and 8. This forms an Obvious Triple. These three cells must contain 2, 5, and 8, so we can eliminate 2, 5, and 8 from all other cells in row 6. If R6C4 had candidates 1, 2, and 5, we would eliminate 2 and 5, leaving only 1.

Example 2: Obvious Triple in a Box

In the middle box, three cells contain only candidates 3, 6, and 9 in various combinations. One cell has all three, another has 3 and 6, the third has 6 and 9. Together, they form an Obvious Triple. We eliminate 3, 6, and 9 from all other cells in that box. This elimination may reveal new placements or enable other techniques.

Example 3: Obvious Triple Leading to Progress

After identifying an Obvious Triple and eliminating candidates from other cells in the unit, one of those other cells might now have only one remaining candidate, allowing immediate placement. This cascading effect is common with Obvious Triples, where one elimination reveals multiple solving opportunities.

Summary

Obvious Triples is an essential intermediate technique that enables significant eliminations in medium to hard puzzles. The key to success is scanning candidate notation to identify when three cells contain only three candidates total. Once found, Obvious Triples provide powerful eliminations that progress puzzles significantly. Practice is essential for developing the pattern recognition skills needed to spot these patterns quickly.

The technique works best when you have complete candidate notation and scan methodically through each unit. Don't rush—careful scanning prevents missing Obvious Triples and ensures accurate identification. As you practice, you'll develop an eye for spotting these patterns more quickly. Obvious Triples often work in combination with other techniques, creating cascading eliminations that significantly progress puzzle solving. Master this technique to improve your efficiency with intermediate puzzles and prepare for more advanced methods.

FAQ (Frequently Asked Questions)

Q1: What's the difference between Obvious Triples and Hidden Triples?

Obvious Triples (Naked Triples) are visually apparent: three cells contain only three candidates total (no other candidates present). Hidden Triples are less obvious: three candidates appear only in three cells, but those cells also contain other candidates. Obvious Triples are easier to spot visually, while Hidden Triples require scanning candidate frequencies. Both enable the same eliminations.

Q2: Do the three cells need to have the same candidates?

No, the three cells can have different combinations of the three candidates. For example, one cell might have all three candidates (2, 5, 8), another might have two (2, 5), and the third might have two different ones (5, 8). As long as the three cells together contain exactly three unique candidates total, it's a valid Obvious Triple.

Q3: How do I know if I've found a valid Obvious Triple?

A valid Obvious Triple requires: (1) exactly three cells in the same unit, (2) these three cells contain only three unique candidates total (in various combinations), and (3) no other candidates appear in these three cells. If you find three cells that together contain exactly three candidates, you've found an Obvious Triple.

Q4: Can Obvious Triples work with more than three candidates?

No, Obvious Triples specifically require exactly three cells containing exactly three candidates. If the three cells contain four or more unique candidates, it's not a valid Obvious Triple. The pattern requires precise matching: three cells, three candidates.

Q5: Are Obvious Triples necessary for all medium puzzles?

Not all medium puzzles require Obvious Triples, but many do. Obvious Triples become necessary when basic techniques and pairs have been exhausted but the puzzle isn't hard enough to require advanced methods. If you're stuck on a medium puzzle and pairs don't apply, look for Obvious Triples. They're often the next logical step.

Q6: How do I avoid missing Obvious Triples?

Systematic scanning is key. Scan each unit (row, column, box) methodically, looking for groups of three cells that together contain only three candidates. Don't rush—careful scanning ensures you don't miss patterns. Some solvers find it helpful to look for cells with few candidates first, as these are more likely to be part of triples.

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For related techniques, check out our guides on Hidden Triples and Intermediate Techniques.

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