Naked Triples & Quads

Extending Naked Pairs to Larger Groups

By Minimal Sudoku Team•Last updated: January 28, 2025

Naked Triples and Naked Quads extend the Naked Pairs logic to groups of 3 or 4 cells. The concept is the same: when N cells contain only N candidates between them, those candidates are claimed by those cells.

Quick Summary

Naked Triple: 3 cells containing at most 3 candidates between them
Naked Quad: 4 cells containing at most 4 candidates between them
Result: Eliminate those candidates from other cells in the unit
Key insight: Not every cell needs all candidates!

The Concept

The Naked Sets rule is simple: N cells with N candidates = those cells claim those candidates.

Pattern	Cells	Candidates
Naked Pair	2 cells	2 candidates
Naked Triple	3 cells	3 candidates
Naked Quad	4 cells	4 candidates

Important: Not All Candidates Required

A Naked Triple doesn't require each cell to have all 3 candidates. For example, cells with (1,2), (2,3), and (1,3) form a valid Naked Triple — the 3 cells collectively contain only candidates 1, 2, 3.

The Golden Rule

👥 Naked Set Rule

When N cells in a unit contain only N candidates between them (each cell has 2 to N of these candidates), eliminate those N candidates from all other cells in the unit.

Naked Triples

A Naked Triple consists of 3 cells that together contain exactly 3 different candidates. These candidates are distributed among the cells — each cell has 2 or 3 of them.

Naked Triple examples (all valid):

Complete:     Incomplete:    Another:
[1,2,3]       [1,2]          [2,5]
[1,2,3]       [2,3]          [2,9]
[1,2,3]       [1,3]          [5,9]

All 3 cells   Only 2 each,   Mixed - still
have all 3   but combined    only 3 unique
             = {1,2,3}       candidates

In all cases, these 3 cells will consume digits 1, 2, and 3 (or 2, 5, 9 in the third example) — so we can eliminate those candidates from other cells in the unit.

Naked Quads

Naked Quads follow the same logic with 4 cells and 4 candidates. They're rarer and harder to spot, but the elimination is more powerful.

Naked Quad example:

Row 3: │ . │[1,4]│ . │[1,2,4]│[2,3]│[1,3,4]│ . │ . │ . │

Cells at positions 2, 4, 5, 6 contain only {1,2,3,4}.
4 cells, 4 candidates = Naked Quad!

→ Eliminate 1, 2, 3, 4 from all other cells in row 3.

How to Find Naked Triples & Quads

Look for small candidate sets

In a unit, identify cells with only 2-4 candidates. These are your building blocks.

Find cells sharing candidates

Look for 3 cells where the union of all candidates is exactly 3 digits. Or 4 cells with exactly 4 digits.

Verify the count

Count unique candidates across all cells. If 3 cells have 3 unique candidates (or 4 cells have 4), you've found a Naked Set.

Eliminate

Remove those candidates from all other cells in the unit.

Start with Pairs

If you find two cells that could be a Naked Pair but have an extra candidate, look for a third cell with that candidate to form a Triple.

Detection Tips

Focus on Small Cells

Cells with only 2-3 candidates are the core of Naked Sets. Ignore cells with 5+ candidates when hunting.

Count Candidates First

Pick any 3 cells in a unit with small candidate counts. Union their candidates — if you get exactly 3 digits, you've found a Naked Triple!

All Must Be in Same Unit

All cells in the Naked Set must share the same row, column, or box. You can't mix cells from different units.

Quads Are Rare

Naked Quads are uncommon. If you've been searching for a while without finding one, try other techniques — they might not exist in your current puzzle.