Hidden Triples

Hidden triples are the sneakier cousin of naked triples. Instead of three cells with only three candidates, hidden triples are three candidates that can only go in three cells — but those cells may have other candidates too, hiding the pattern.

What is a Hidden Triple?

A hidden triple occurs when three candidates in a unit can only appear in exactly three cells, even if those cells contain other candidates.

Example: If 2, 5, and 8 can only go in cells A, B, and C of a row, that's a hidden triple — even if those cells also contain other candidates like 3, 6, and 9.

The triple is "hidden" because extra candidates mask the pattern.

Hidden Triples vs. Naked Triples

Both are equally powerful — they're just found differently!

Visual Example

Before elimination:

Finding the hidden triple:

Where can each digit go in this row?

• 2: cells A, C only
• 5: cells A, C, E
• 8: cells C, E only

Together, digits 2, 5, and 8 can only go in cells A, C, and E. That's a hidden triple!

After elimination:

Now the hidden triple becomes a visible naked triple!

The Logic Explained

Think about it step by step:

1. The 2 must go somewhere in this row
2. The only cells that can have 2 are A and C
3. The 5 must also go somewhere
4. The only cells for 5 are A, C, and E
5. The 8 must also go somewhere
6. The only cells for 8 are C and E
7. Three digits, three cells — each cell gets one digit
8. So A, C, and E can ONLY contain 2, 5, or 8

The result: Remove all other candidates from cells A, C, and E!

Common Hidden Triple Patterns

Pattern 1: The "Full Spread"

All three digits appear in all three cells:

Pattern 2: The "Triangle" Pattern

Each pair of digits shares different cells:

The distribution:

• 2: appears in cells A and E
• 5: appears in cells A and C
• 8: appears in cells C and E

Together they're still confined to exactly three cells!

Pattern 3: The "Nearly Naked"

After cleanup, you get a visible naked triple:

Before:

After:

Hidden Triples in Boxes

Boxes are prime territory for hidden triples:

Where can each digit go?

• 1: cells A, C only
• 4: cells A, C, E
• 7: cells C, E only

Hidden triple! Eliminate other candidates from A, C, E:

How to Find Hidden Triples

Method 1: Digit Mapping

1. Pick a unit (row, column, or box)
2. For each digit, list which cells can hold it
3. Find three digits that share exactly three cells
4. That's your hidden triple!

Example mapping:

• 1: cells A, C
• 2: cells B, D, F
• 3: cells B, D, G
• 4: cells A, C, E
• 5: cells B, F
• 6: cells D, G
• 7: cells C, E
• 8: cells F, G
• 9: cells B, D, F

Check combinations:

• 1, 4, 7: cells A, C + A, C, E + C, E = A, C, E (3 cells!) ✓

Method 2: Focus on Rare Digits

1. Find digits that appear in only 2-3 cells
2. These are most likely to form hidden triples
3. Combine them and check if total cells = 3

Method 3: Complement Approach

In a unit with 6 empty cells:

1. If you find a naked triple, the other 3 cells have a hidden triple
2. Work backwards from what you CAN see

Step-by-Step Example

Given this box:

Step 1: Map each digit

• 1: A, B, G, H, I
• 2: B, H, I
• 3: A, B, E, G, H
• 4: A, G
• 5: A, E, G, I
• 7: A
• 9: E, H, I

Step 2: Look for three digits in three cells

• 4: A, G (only 2 cells)
• 7: A (only 1 cell)
• 9: E, H, I (3 cells)

Can we combine?

• 4, 7: A, G — only 2 cells total, need another digit
• What else appears only in A and/or G? Check 5: A, E, G, I — has extra cells

Let's try: 2, 3, 9

• 2: B, H, I
• 3: B, E, G, H — has 4 cells, too many

Try: 4, 5, 7

• 4: A, G
• 5: A, E, G, I — 4 cells
• Too many cells

This box may not have a clean hidden triple — that's okay! Not every unit has one.

The Elimination Process

Once you find a hidden triple:

1. Verify the pattern — All three digits in exactly three cells?
2. Remove other candidates — Delete non-triple digits from triple cells
3. Check for singles — Did any cell become a single?
4. Apply naked triple — The cleanup often reveals naked triple eliminations
5. Look for new patterns — The board changed!

Practice Exercises

Exercise 1: Find the hidden triple

Exercise 2: Find the hidden triple in this box

Common Mistakes

Mistake 1: Wrong elimination direction

• Hidden triple: eliminate OTHER candidates FROM triple cells
• NOT: eliminate triple candidates from OTHER cells
• That's what naked triples do!

Mistake 2: Missing a cell

If a digit appears in a 4th cell you missed, it's not a valid hidden triple. Always double-check your mapping.

Mistake 3: Stopping too early

After cleaning up a hidden triple:

1. It becomes a naked triple
2. Apply the naked triple eliminations too
3. Check for new singles

Mistake 4: Forcing patterns

Not every unit has a hidden triple. If you can't find one, move on to other techniques.

Mistake 5: Incomplete digit check

All three digits must be checked. If you verify only two, you might miss that the third appears elsewhere.

Complementary Patterns

In a unit with 6 empty cells:

Why this matters:

• Sometimes the naked version is easier to spot
• Sometimes the hidden version is easier
• Finding one automatically gives you the other!

When Hidden Triples Appear

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

Quick Reference

Hidden triple definition:

• 3 digits that can only appear in 3 cells
• Those cells may have other candidates
• Other candidates are eliminated from the triple cells

Finding hidden triples:

1. Map each digit to its possible cells
2. Find 3 digits sharing exactly 3 cells
3. Verify no digit appears in a 4th cell

Elimination rule:

• Remove non-triple candidates from triple cells
• NOT: remove triple candidates from other cells

When to look:

• Cells have many candidates (4+)
• Naked patterns aren't visible
• After basic techniques stall

What's Next?

Once you master hidden triples:

• Hidden Quads — Four candidates in only four cells
• X-Wing — Cross-row/column elimination pattern
• Pointing Pairs — Box/line intersection techniques