In a 9-cell unit (a row, a column, or a 3x3 block), if three of the cells have a total of three digits as candidates, then these three digits must each occupy one of these three cells and cannot occupy other cells in the same 9-cell unit. So if these three digits appear in other cells in the same 9-cell unit as candidates, they can be removed. Note that it is not necessary that each of these three cells has all three digits as candidates, nor that each of the three digits is a candidate for all three cells. It is only required that the three cells have only these three digits in total as candidates. We will demonstrate this technique visually with the following examples.
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In row R7 of the puzzle in Figure 1a, the three green cells (R7,C4), (R7,C6), and (R7,C7) have a total of three digits 1, 4, and 7 as candidates. That means each of these three cells has at most three candidate digits (marked in red), which are all from digits 1, 4, and 7. As a consequence, the digits 1, 4, and 7 each will occupy one of these three green cells and cannot occupy any other cells in the same row. Therefore, the candidates 1, 4, and 7, if any in other cells in the same row, can be removed, as shown in Figure 1b below.
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In column C6 of the puzzle in Figure 2a, the three green cells (R4,C6), (R5,C6), and (R8,C6) have a total of three digits 2, 8, and 9 as candidates. That means each of these three cells has at most three candidate digits (marked in red), which are all from digits 2, 8, and 9. As a consequence, the digits 2, 8, and 9 each will occupy one of these three green cells and cannot occupy any other cells in the same column. Therefore, the candidates 2, 8, and 9, if any in other cells in the same column, can be removed, as shown in Figure 2b below.
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In block B6 of the puzzle in Figure 3a, the three green cells (R6,C7), (R6,C8), and (R6,C9) have a total of three digits 3, 5, and 7 as candidates. That means each of these three cells has at most three candidate digits (marked in red), which are all from digits 3, 5, and 7. As a consequence, the digits 3, 5, and 7 each will occupy one of these three green cells and cannot occupy any other cells in the same block. Therefore, the candidates 3, 5, and 7, if any in other cells in the same block, can be removed, as shown in Figure 3b below.
4
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List of Sudoku Solving Techniques
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