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Naked Triple

Naked TripleSTEP 0/3

Introduction

Time for the next level of the Naked Triple strategy. It works similarly to Naked Pairs, but instead of two cells and two candidates, we use three cells and three candidates.

We look for an area (row, column, or box) containing exactly three cells that together contain no more than three different candidates.
These three candidates must be distributed among these three cells. They can appear in different combinations, such as {5, 8, 9}, {5, 8}, and {5, 9}.

Since these three specific candidates are reserved for these three cells, we can remove them from all other cells in the same area.

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Naked TripleSTEP 1/3

Finding the Triple

Look at Row 5. Here we find three cells that together form an interesting candidate pattern.

In Row 5, Column 4, we have candidates 5, 8, and 9.
In Row 5, Column 5, we have candidates 5 and 8.
In Row 5, Column 6, we have candidates 5 and 9.

Together, these three cells contain exactly three different candidates: 5, 8, and 9.

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Naked TripleSTEP 2/3

Finding the Relationship

Now for the most important part: the digits 5, 8, and 9 must be distributed among these three cells.

Candidate 8 can only appear in Row 5, Column 4 or Row 5, Column 5.
Candidate 9 can only appear in Row 5, Column 4 or Row 5, Column 6.
Candidate 5 appears in all three cells, but regardless of its final position, all three digits must be placed in exactly these three cells.

This means that no other cell in Row 5 can contain candidates 5, 8, or 9.

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Naked TripleSTEP 3/3

Analysis

We do not need to know which of the three cells will receive 5, which will receive 8, and which will receive 9. What matters is that all three digits are confined to our triple.

All possible combinations still use only the digits 5, 8, and 9 in these three cells.
None of the remaining cells in Row 5 is needed to place these three candidates.

Our triple therefore works like a reservation of three seats - the digits 5, 8, and 9 are already reserved for these three specific cells.

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