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Sudoku Algorithms
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Hidden Quads
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The Hidden Quads Sudoku patterns are similar to the Hidden Triples. As the name suggests, Hidden Quads have four candidates located in four cells. Like Hidden Triples, Hidden Quads do not require that each cell has all four selected candidates, but all other cells in the unit should not have any of the selected candidates. Similar to the Hidden Triples, Hidden Quads have interrelated Naked patterns in the same unit.
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Hidden Quads In Square
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The two images below show the interrelated Hidden Quads on the left and Naked Triples in Square on the right.
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The first 3x3 square in the first row has a Hidden Quads pattern. Four candidates '1', '6', '8', and '9' are marked in yellow in four cells B1, B2, C2, and C3. According to the Hidden Quads rules, we can remove candidate '3' marked in red in cells C2 and C3. The image on the right shows the related Naked Triple pattern in the same square. It has three candidates '3', '4', and '5' marked in yellow in cells A1, A2, and A3, allowing us to remove the same candidate '3' marked in red in cells C2 and C3.
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Hidden Quads In Row
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A Hidden Quads pattern on the left and the related Naked Triples pattern in Row F on the right are shown in the images below.
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A Hidden Quads pattern in Row F has four candidates '2', '3', '5', and '9' marked in yellow in cells F4, F6, F8, and F9. The Hidden Quads rules allow us to remove additional candidates '1' and '6' marked in red in the pattern’s cells. The related Naked Triples candidates '1', '4', and '6' are marked in red in cells F1, F3, and F5 in the image on the right. This pattern, similar to the related Hidden Quads, allows us to remove candidate '6' marked in red in cells F4 and F6, and '1' in cells F8 and F9.
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Hidden Quads In Column
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The images below show an example of two interrelated Quads. There is a Hidden Quads pattern in Column 6 on the left and a related Naked Quads pattern in the same column on the right.
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A Hidden Quads pattern has four candidates '4', '5', '7', and '8' marked in yellow in four cells E6, F6, G6, and I6 in Column 6. The additional candidates '1', '2', '3', and '6' marked in red in the Hidden Quads cells should be removed. The Naked Quads pattern has candidates '1', '2', '3', and '6' marked in yellow in four cells A6, C6, D6, and H6 in Column 6. This allows us to remove the candidates '1', '2', '3', and '6' marked in red in the right image as well.
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Hidden Quintets
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A Hidden Quintets pattern is similar to a Hidden Quads pattern, but it has five candidates located in five cells in the same unit.
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Hidden Quintets In Square
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The following example shows a Hidden Quintets pattern in the middle 3x3 square in the first row in the left image and the related Naked Triples pattern in the same square in the right image.
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The Hidden Quintets pattern has candidates '1', '4', '3', '8', and '9' marked in yellow in five cells A4, A6, B4, B6, and C4 in the square in the left image. This allows the removal of candidate '7', marked in red, from the Hidden Quintets cells B4, B6, and C4. The related Naked Triple pattern has candidates '2', '5', and '7' marked in yellow in cells A5, B5, and C5 in the right image, allowing us to remove candidate '7', marked in red, in cells B4, B6, and C4.
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Hidden Quintets In Row
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The following images show an example of interrelated Hidden Quads on the left and Naked Triples on the right in Row A.
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A Hidden Quintets pattern on the left has five candidates '1', '4', '5', '6', and '8' marked in yellow in five cells A1, A2, A3, A4, and A6. Candidate '9', marked in red, in cell A6 should be removed. The related Naked Triples pattern has candidates '2', '3', and '9' marked in yellow in the right image in cells A5, A7, and A9 in Row A. The Naked Triples pattern also allows us to remove the candidate '9' in cell A6.
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Hidden Triples In Column
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The image below presents Hidden Quintets and related Naked Triples Sudoku patterns in the column.
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A Hidden Quintets pattern in Column 6 in the left image has five candidates '4', '5', '6', '8', and '9' marked in yellow in cells A, B, D, F, and I of Column 6. Candidate '1', marked in red, can be removed in cells A, D, and F of Column 6. In the right image, a related Naked Triple pattern with candidates '1', '2', and '3' is marked in yellow in cells C, E, and H of Column 6, allowing us to remove the same candidate '1'.
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