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Hidden Pairs and Triples

The hidden pairs technique is a powerful candidate elimination technique similar to the naked pairs technique. A hidden pair is a pair of cells in the same group which contain two candidates which don't occur in any other cells of the group. This means that neither of the cells can contain any other candidates. An example is shown below:

The two cells highlighted in red form a hidden pair with the candidate values 3 and 5. No other cells in that column can contain either a 3 or a 5, so we can remove the candidates 1 and 9 from the top cell.

Hidden triples are also possible, where a group of three cells contain three values that can't occur elsewhere in a group, but like naked triples, these are extremely rare, provided you look for naked pairs first. On an aside, hidden tuples (pairs, triples etc...) are the dual of naked tuples, meaning that for every hidden tuple there is a corresponding naked tuple. In this case, the other three cells in the column form a naked triple of 1,4 and 9 which can be used to make the same elimination. In theory, you therefore never need to use the hidden pairs technique, but it can be useful in spotting an elimination.

Once you have mastered the techniques we've seen so far (hidden singles, intersection reduction, naked singles, naked pairs and triples and hidden pairs and triples), you will be able to solve any "Hard" sudoku generated by Puzzle Tiger.

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