In a 9-cell unit (a row, a column, or a 3x3 block) of a Sudoku puzzle, we look for a certain digit "k" that is a candidate in exactly two cells. That means the digit "k" has two possible positions in the 9-cell unit. If both cases lead to the same conclusion (that is, some other candidate digits eliminated or confirmed in some other cells), then that conclusion must be true.
The example below demonstrates the Coloring technique that leads to eliminating a candidate digit in a cell.
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In block B2 of this puzzle, the digit 1 is a candidate for exactly two cells (R2,C4) and (R2,C6). That means there are two possible positions for the digit 1 in this 3x3 block, and one of these two cells (R2,C4) and (R2,C6) must be 1. Let's see what conclusion we can draw with the Coloring technique.
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In the first case, suppose that the cell (R2,C4) is 1.
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Since the cell (R2,C4) is 1, it cannot be 4. The candidate digit 4 in cell (R2,C4) is eliminated.
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The cell (R3,C4) must be 4 since it is the only possible position for the digit 4 in column C4.
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The cell (R3,C2) cannot be 4 since the cell (R3,C4) in the same row R3 is 4. As a result, the cell (R3,C2) must be 6, as it turns out to be the only candidate for the cell.
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The cell (R5,C2) cannot be 6 since the cell (R3,C2) in the same column C2 is 6.
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In the second case, suppose that the cell (R2,C6) is 1.
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The cell (R5,C6) cannot be 1 since the cell (R2,C6) in the same column C6 is 1. As a result, the cell (R5,C6) must be 6, as it turns out to be the only candidate for the cell.
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The cell (R5,C2) cannot be 6 since the cell (R5,C6) in the same row R5 is 6.
As we can see in both cases, the cell (R5,C2) cannot be 6. We can conclude that the candidate digit 6 in cell (R5,C2) can be eliminated, as shown in Figure 4.
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The example above shows how we can eliminate a candidate from a cell with this technique. Actually, this technique can be used to confirm a digit for a cell as well. We will demonstrate that scenario here: Coloring (candidate confirmed)
List of Sudoku Solving Techniques
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