Hidden Triple Technique: Finding Three Hidden Candidates

Hidden Triple is an advanced version of Hidden Pairs and a more complex intermediate Sudoku technique. The core idea is: when three candidates appear only in the same three cells of a unit (row, column, or box), those three cells must contain these three numbers, so you can eliminate all other candidates from these three cells.

Before reading this article, we recommend understanding Sudoku naming conventions and Hidden Pairs technique.

Example 1: Hidden Triple in a Row

Let's look at the first example, finding a hidden triple in Row 6.

Figure 1: Hidden Triple in Row 6

Current Grid Data

Based on the CSV81 format candidate data, Row 6 looks like this:

• R6C1: Candidates {2, 4}
• R6C2: Filled with 5 (b5 means confirmed as 5)
• R6C3: Candidates {2, 4}
• R6C4: Candidates {3, 4, 9}
• R6C5: Candidates {6, 8}
• R6C6: Candidates {3, 6, 8}
• R6C7: Candidates {3, 7, 8}
• R6C8: Candidates {2, 3, 9}
• R6C9: Candidates {3, 6, 7}

Analysis Process

Example 2: Hidden Triple in a Box

Now let's look at another example, finding a hidden triple in Box 6.

Figure 2: Hidden Triple in Box 6

Current Grid Data

Based on the CSV81 format candidate data, Box 6 (Rows 4-6, Columns 7-9) looks like this:

• R4C7: Filled with 9 (b9 means confirmed as 9)
• R4C8: Candidates {1, 2, 7}
• R4C9: Candidates {1, 3, 7}
• R5C7: Filled with 6 (g6 means confirmed as 6)
• R5C8: Candidates {1, 2, 3, 7}
• R5C9: Filled with 9 (g9 means confirmed as 9)
• R6C7: Filled with 9 (b9 means confirmed as 9)
• R6C8: Candidates {3, 5}
• R6C9: Filled with 2 (g2 means confirmed as 2)

Analysis Process

Hidden Triple vs Hidden Pair

Let's compare Hidden Pairs and Hidden Triples:

How to Find Hidden Triples

Finding Hidden Triples requires systematic and patient analysis:

Variations of Hidden Triples

Hidden Triples can appear in different forms:

• Complete type: Each cell contains some or all of the three numbers. Example: {1,2,7}, {1,2,7}, {1,2,7}
• Distributed type: The three numbers are distributed across the three cells. Example: {1,2}, {2,7}, {1,7}
• Mixed type: Some cells contain all three numbers, others only some. Example: {1,2,7}, {1,7}, {1,2,7}

Regardless of the form, the key is that these three numbers appear only in these three cells and not in other cells of that unit.

Technique Summary

Key points for applying Hidden Triple:

• Perspective: Observe from the number distribution angle, tracking where three numbers appear
• Recognition: Three candidates appear only in the same three cells within a unit
• Elimination target: Other candidates in these three cells
• Analysis method: Requires systematic, patient tracking of each candidate's distribution in the unit
• Difficulty: Harder to spot than Hidden Pairs, requires more careful observation
• Practical value: In complex difficult puzzles, can be the key technique to break through bottlenecks

Advanced: Comparison with Naked Triples

The counterpart to Hidden Triples is Naked Triples: When three cells in a unit have candidates that are all subsets of the same three numbers (like {1,2}, {2,7}, {1,7}), you can eliminate these three numbers from other cells in that unit.

Key difference:

• Naked Triple: Look at cell candidates, eliminate these three numbers from other cells
• Hidden Triple: Look at number distribution, eliminate other candidates from these three cells themselves