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Sudoku Algorithms
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Hidden Triples
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Hidden Triples are very similar to Hidden Pairs. While Hidden Pairs consider a list of two candidates, Hidden Triples involve three candidates located in only three cells within the same 3x3 square, row, or column. The Hidden Triples cells have additional candidates, making these triples "hidden" among other candidates. According to the Hidden Triples rules, all the additional candidates in those three cells can be removed. Unlike Hidden Pairs, all three cells in Hidden Triples are not required to contain all three candidates. However, each selected candidate should be present in at least two of these cells and should not appear in any additional cell of the unit.
All Sudoku Hidden patterns (such as Hidden Triples, Hidden Quads, etc.) are somewhat similar to Naked patterns (like Naked Triples, Naked Quads, etc.) and are interrelated. If there is a Hidden pattern in any Sudoku unit, this unit also has a Naked pattern and vice versa, and both patterns allow us to eliminate the same set of candidates.
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Hidden Triples In Square
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The two images below show an example of the Hidden Triples in a Square pattern and the interrelated Naked Triples in a Square pattern. The Hidden Triples pattern appears in cells F1, F2, and F3 because there is a Naked Triples pattern in cells E1, E2, and E3, and vice versa. Both patterns allow the elimination of the same set of possible candidates marked in red in cells F2 and F3.
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The image on the left shows the Hidden Triples ('6' and '8' in F1, '1' and '6' in F2, and '1' and '8' in F3) marked in yellow in the first 3x3 square in the second row. Since the three candidates 6, 1, and 8 only appear in cells F1, F2, and F3, no other candidates can be placed in those three cells. We can remove an additional candidate '7', marked in red, in cells F2 and F3.
The image on the right shows a Sudoku Naked Triple pattern in cells E1, E2, and E3 with candidates '5', '9', and '7' marked in yellow. According to Naked Triple pattern rules, we can remove hint '7', marked in red, in cells F2 and F3.
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Hidden Triples In Row
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The two images below show an example of the Hidden Triples in Row (on the left) and the interrelated Naked Pairs in Row (on the right).
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The image on the left shows Hidden Triples '1', '7', and '9' marked in yellow in Row A (in cells A2, A3, and A6). We can remove the additional candidates '3' and '6' marked in red in the Hidden Triples pattern cells A2, A3, and A6. The related Naked Pairs in Row, shown in the picture on the right, are marked in yellow in cells A3 and A6. The Naked Pairs pattern rules allow us to remove all other appearances of the candidates '3' and '6' marked in red in Row A.
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Hidden Triples In Column
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The following two images show the interrelated Hidden Triples pattern on the left and Naked Pairs in Column on the right.
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The image on the left shows the Hidden Triples pattern ('6' and '7' in cell C4, '3' and '7' in cell E4, and '3' and '6' in cell I4) marked in yellow in Column 4. According to the Hidden Triples rules, we can remove the candidates '2' and '9' marked in red in cell E4. The related Naked Pairs pattern is shown in the image on the right. Candidates '2' and '9' marked in red in cells A4 and G4 should be removed as well according to the Naked Pairs rules.
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