Naked Triples

Naked triples extend the naked pair concept to three cells. Once you've mastered pairs, triples follow the same logic — just with one more cell and one more candidate.

What is a Naked Triple?

A naked triple occurs when three cells in the same unit (row, column, or box) contain only candidates from a set of three numbers.

Key insight: The three cells don't each need all three candidates. They just need to collectively cover exactly three numbers.

Example: Cells with [2,5], [5,8], and [2,8] form a naked triple on 2, 5, 8.

Valid Naked Triple Combinations

A triple of digits [2, 5, 8] can appear as:

What matters:

• Exactly three cells
• Only candidates from a set of three digits
• Each digit must appear in at least one of the three cells
• NO extra candidates allowed in any cell

Visual Example

Before elimination:

Finding the triple:

1. Cell B has [3,6] — two of our triple's digits
2. Cell D has [1,6] — two of our triple's digits
3. Cell F has [1,3,6] — all three digits

Together they contain only 1, 3, and 6 — that's a naked triple!

After elimination:

The Logic Explained

Think about it step by step:

1. Cells B, D, and F can only contain 1, 3, or 6
2. There are three cells and three numbers
3. Each cell will get exactly one number
4. We don't know which cell gets which number yet
5. But we DO know that 1, 3, and 6 are taken by these three cells

The result: No other cell in the row can have 1, 3, or 6. They're "claimed" by the triple!

Common Triple Patterns

Pattern 1: The "Full House" Triple

All three cells have all three candidates:

Why it's easy: Three identical cells immediately stand out.

Pattern 2: The "Split" Triple

Candidates are distributed across cells:

Why it works: Each pair of digits appears, linking all three cells.

Pattern 3: The "Anchor" Triple

One cell has all three, others have two:

Why it works: The "full" cell anchors the pattern; the others confirm it.

Pattern 4: The "Minimalist" Triple

One or more cells may have only one candidate:

Why it works: Even a single candidate cell participates in the triple.

Naked Triples in Boxes

Triples in boxes are common and powerful:

After elimination:

Double Coverage

The best naked triples affect multiple units at once!

If a naked triple in a box also shares a row or column:

What this means:

• Eliminate 1, 3, 6 from other cells in the box
• AND eliminate 1, 3, 6 from other cells in that row

How to Find Naked Triples

Method 1: Start with Small Cells

1. Scan for cells with exactly 2 candidates
2. Note the digits involved
3. Look for other cells in the same unit with subsets of these digits
4. If three cells collectively use exactly three digits, you have a triple

Example thought process:

• "Cell B has [3,6]"
• "Is there a [1,3], [1,6], [3,6], or [1,3,6] nearby?"
• "Cell D has [1,6] — that adds 1 to our set"
• "Now I need [1,3], [3,6], or [1,3,6] for the third cell"
• "Cell F has [1,3,6] — perfect!"

Method 2: Candidate Grouping

1. Pick a unit (row, column, or box)
2. List all candidates for all empty cells
3. Look for three digits that appear together frequently
4. Check if exactly three cells contain only those digits

Method 3: Build from a Pair

1. Find a naked pair
2. Look for a third cell that adds exactly one new digit
3. Check if all three cells together have only three digits

Example:

• Find pair [2,5] and [2,5]
• Look for cell with [2,8], [5,8], or [2,5,8]
• If found, you might have a triple on 2, 5, 8

Method 4: Look for Clusters

With practice, triples become visual:

• A cluster of cells with limited, overlapping candidates
• The candidates keep appearing together
• Other cells in the unit have different candidates

The Elimination Process

Once you find a naked triple:

1. Identify the shared unit(s) — row, column, box, or multiple
2. Check each other cell in that unit — does it have any triple candidate?
3. Remove those candidates — cross them off
4. Check for singles — did any cell become a single?
5. Look for new patterns — the elimination might reveal more pairs or triples!

What the Triple Does NOT Affect

Important: The naked triple only affects cells in units that all three triple cells share.

Triples vs. Pairs

When to look for triples:

• Pairs aren't visible
• A unit has many cells with 2-3 candidates
• You've made eliminations but no singles emerged

Practice Exercises

Exercise 1: Find the naked triple

Exercise 2: Find the triple in this box

Common Mistakes

Mistake 1: Including cells with extra candidates

A cell with [2,5,8,9] cannot be part of a [2,5,8] triple. The 9 disqualifies it.

Mistake 2: Eliminating from the triple cells

NEVER remove candidates from the triple cells themselves. They need to keep their candidates!

Mistake 3: Forgetting to eliminate from all cells

Eliminations apply to all other cells in the unit, not just nearby ones.

Mistake 4: Missing triple extensions

If a triple's three cells also align in a row or column within a box, eliminate from that row/column too.

Mistake 5: Confusing with hidden triples

Mistake 6: Not following up

After eliminating, check for new singles immediately. The elimination might solve cells!

When Naked Triples Appear

• Easy puzzles: Rarely needed
• Medium puzzles: Occasionally useful
• Hard puzzles: Common technique
• Expert puzzles: Essential and frequent

What's Next?

Once you master naked triples:

• Naked Quads — Same idea with four cells and four candidates
• Hidden Triples — The reverse: three candidates that can only go in three cells
• Pointing Pairs — Box/line intersection techniques