Sudoku Techniques (Part 6) – Naked Triples and Quads

I was very tempted to put Naked Triplets in the title for this post after seeing the traffic that “Naked Pairs” generated. I can’t imagine why there would have been such a boost….I leave that as an exercise for the reader.

Naked Triples (and quads) is another sudoku technique that will help you clear out the grid on your way to mastery as you learn how to play sudoku. It builds on the idea of naked pairs, where you found just two cells in a house, containing exactly the same two candidates.

For naked triples, you should look for three cells in the same house containing the same three candidate or a combination of those candidates….read that last bit again closely. I have highlighted two sets of naked triples in the diagram below.

Naked Triples

In the centre box, you can see the most obvious example of this technique. Three cells, all containing exactly the same three candidates 2,5 and 9. In the second case, in column 6, the candidates are 1,2 and 5 but you can see that two of the cells do not contain all candidates.

In fact, I have found that this is more often the case than the first one. My own personal favorite is where you end up with three pairs of values that “cycle” round the triple. So, for example, you may see 1,3 then 3,5 and finally 5,3 – looping round to join up the triple.

Now that we have the triples, we can immediately remove the candidates 2 and 5 from the other cells in the middle box, leaving just 6 and 8. It is a shame in this case that the two triples help us with exactly the same cells in the middle box.

A naked quad builds again and has 4 candidates in 4 cells all the same (or subsets thereof!). I tend to find that once you get to naked quads, the rest of the house is already completed and so you gain very little but bear it in mind for those rare cases. In the diagram above you can see a naked quad in box 9 and sure enough, the rest of the values are filled in.

See if you can spot a naked triple in a harder puzzle this weekend….if you read the Sunday Times, I will be interested to hear your experiences.

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