Hidden Triples
An intermediate technique where three numbers can only appear in three specific cells within a region, allowing for candidate elimination.
What Are Hidden Triples?
A Hidden Triple occurs when three numbers can only appear in three specific cells within a row, column, or box. These three numbers are "hidden" among other candidates, but once identified, all other candidates can be eliminated from these three cells.
Key Concept
Hidden Triples are the inverse of Obvious Triples. Instead of focusing on cells that share the same candidates, we focus on numbers that can only go in the same three cells.
Example: Numbers 1, 2, and 3 form a Hidden Triple in cells A, B, and C
How to Identify Hidden Triples
The Process
- 1 Focus on a specific row, column, or box
- 2 For each number, identify which cells it can appear in
- 3 Look for three numbers that can only appear in the same three cells
- 4 Eliminate all other candidates from these three cells
Detection Strategy
💡 Pro Tip: Look for numbers that have limited placement options in a region.
Visual Example
In this column example, numbers 2, 5, and 8 can only appear in the first three cells, forming a Hidden Triple.
Before: Identify the Hidden Triple
Numbers 2, 5, and 8 (highlighted in purple) can only appear in the first three cells of this column
After: Eliminate Other Candidates
After elimination, the first three cells only contain candidates 2, 5, and 8
Hidden vs. Obvious Triples
Hidden Triples
- • Focus on numbers and where they can go
- • Three numbers constrained to three cells
- • Eliminate other candidates from those cells
- • Numbers are "hidden" among other candidates
Obvious Triples
- • Focus on cells and what they contain
- • Three cells constrained to three numbers
- • Eliminate those numbers from other cells
- • Numbers are "obvious" in the cells
Key Insight: Hidden and Obvious Triples are complementary techniques. What appears as a Hidden Triple from one perspective may be an Obvious Triple from another!
When to Use Hidden Triples
Best Situations
- ✓ When cells have many candidates (4+ each)
- ✓ When obvious techniques aren't working
- ✓ In regions with limited placement options for some numbers
- ✓ In harder puzzles where elimination is key
Common Mistakes
- × Not systematically checking each number's placement options
- × Confusing with Obvious Triples
- × Missing the pattern when it spans different candidate positions
- × Eliminating from wrong cells
Practice Tips
Development Strategy
- 1. Master Hidden Pairs first
- 2. Practice mapping numbers to possible cells
- 3. Look for constrained number placements
- 4. Always verify eliminations are correct
Analysis Method
- • Create a "where can number X go" chart
- • Look for numbers with 2-3 placement options
- • Check if multiple numbers share the same cells
- • Practice on puzzles with many candidates
Related Techniques
Ready to Practice Hidden Triples?
Challenge yourself with puzzles that require intermediate elimination techniques.