The Naked Quad technique is similar to the Naked Triplet technique. Instead of three cells and three digits for the Naked Triplet technique, the Naked Quad technique involves four cells and four digits.
In a 9-cell unit (a row, a column, or a 3x3 block), if four of the cells have a total of four digits as candidates, then these four digits must each occupy one of these four cells and cannot occupy any other cells in the same 9-cell unit. So if these four digits appear in other cells in the same 9-cell unit as candidates, they can be removed. Just like in Naked Triplet, it is not necessary that each of these four cells has all four digits as candidates, nor that each of the four digits is a candidate for all four cells. It is only required that the four cells have only these four digits in total as candidates.
Let's use the following examples to demonstrate this technique visually.
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6
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In row R5 of the puzzle in Figure 1a, the four green cells (R5,C4), (R5,C5), (R5,C6), and (R5,C7) have a total of four digits 1, 3, 6, and 9 as candidates. That means each of these four cells has at most four candidate digits (marked in red), which are all from digits 1, 3, 6, and 9. As a consequence, the digits 1, 3, 6, and 9 each will occupy one of these four green cells and cannot occupy any other cells in the same row. Therefore, the candidates 1, 3, 6, and 9, if any in other cells in the same row, can be removed, as shown in Figure 1b below.
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In column C4 of the puzzle in Figure 2a, the four green cells (R2,C4), (R3,C4), (R5,C4), and (R9,C4) have a total of four digits 1, 2, 5, and 8 as candidates. That means each of these four cells has at most four candidate digits (marked in red), which are all from digits 1, 2, 5, and 8. As a consequence, the digits 1, 2, 5, and 8 each will occupy one of these four green cells and cannot occupy any other cells in the same column. Therefore, the candidates 1, 2, 5, and 8, if any in other cells in the same column, can be removed, as shown in Figure 2b below.
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In block B9 of the puzzle in Figure 3a, the four green cells (R8,C7), (R8,C8), (R8,C9), and (R9,C9) have a total of four digits 1, 2, 5, and 7 as candidates. That means each of these four cells has at most four candidate digits (marked in red), which are all from digits 1, 2, 5, and 7. As a consequence, the digits 1, 2, 5, and 7 each will occupy one of these four green cells and cannot occupy any other cells in the same block. Therefore, the candidates 1, 2, 5, and 7, if any in other cells in the same block, can be removed, as shown in Figure 3b below.
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List of Sudoku Solving Techniques
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