Hidden Triples

In the same way we have extended Naked Pairs to Naked Triples, we can extend Hidden Pairs to Hidden Triples. The rule stays the same: if a total of three candidates are only seen in exactly three cells within a house (row, column or square), then we know that these three candidates will be in the cells. We do not know in which order, but we can eliminate all other candidates in these three cells.

Hidden Triples - Example 1

Let us consider the following example. Column 6 has a Hidden Triple formed by the cells A6, B6 and C6. The candidates triple {3, 4, 7} is contained in all three cells and nowhere else in the column. Hence, the triple will surely be the values in these three cells in some order. What we know for sure is that the other candidates are not possible for these three cells and we can eliminate them.

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Hidden Triples - Example 2

Similarly to Naked Triples, the three candidates, which form the triple, should not necessarily be present in all 3 cells. More generally we are interested in a group of 3 cells which contain a total of three candidates and the candidates are not seen anywhere else.

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In the following example, we consider the middle-left box. The triple consists of cells D1, D2 and D3 with candidates {4, 7, 8}. Observe that the cell D2 does not contain the candidate 8. Nevertheless, the group of three cells contains all three candidates and they are not seen anywhere else in the square. Hence, no other candidates can be present in the three cells and we can eliminate them. In this example, the number of candidates present in the cells is 3-2-3.
In the same way we have formed Naked Triples, we can find Hidden Pairs for any such combination of two or three candidates per cell. We are only concerned with the total number of candidates, which should be three, among the three cells.