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 Naked Triples

# Naked Triples

We can certainly extend Naked Pairs to Naked Triples.  Any three cells in the same unit that contain the same three candidate numbers will be a Naked Triple. The rest of the unit can be scrubbed clean of any of those numbers.

But a Naked Triple is much more versatile than this rule implies.  In fact it  is not necessary for there to be three candidates in each cell.  As long as there are in total three candidates in three cells.  Obviously we’re not going to apply this rule to single candidate cells – since they are solved, so the possible combinations are as follows:

 The combinations of candidates for a Naked Triple will be one of the following: (123) (123) (123) (123) (123) (12) (123) (12)  (23) (12)  (23)  (13)

The last case is interesting and the advanced strategy XY-Wings uses this formation (but that’s skipping way ahead).

Let’s look at an example:

Fig. 5.1

Here we have a Naked Triple in Row E with the values 5/7/8.  Number 5 is excluded from E1 but in combination 5/7/8 must fill the cells circled.  There are no other possibilities.  As the triple is aligned on a Row we can remove any 5 or 7 or 8 on that row. These are marked.  We get a solution of 1 on E2 which must help us carry on.

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