The logic of the Forcing Chain technique is very similar to the Coloring technique. But for this technique, we look for a cell that has exactly two candidate digits.
Suppose that a certain cell in the Sudoku puzzle has exactly two candidate digits "m" and "n". So, that cell must be either "m" or "n". 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 Forcing Chain technique that leads to eliminating a candidate digit in a cell.
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In this puzzle, the cell (R4,C4) has two candidate digits 1 and 4. That means there are two possibilities for this cell. It can be either 1 or 4, but not others. Let's see what conclusion we can draw with the Forcing Chain technique.
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In the first case, suppose that the cell (R4,C4) is 1.
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The cell (R5,C5) cannot be 1 since the cell (R4,C4) in the same block B5 is 1.
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The cell (R3,C4) cannot be 1 since the cell (R4,C4) in the same column C4 is 1. As a result, the cell (R3,C4) must be 7, as it turns out to be the only candidate for the cell.
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The cell (R1,C5) cannot be 7 since the cell (R3,C4) in the same block B2 is 7. As a result, the cell (R1,C5) must be 3, as it turns out to be the only candidate for the cell.
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The cell (R5,C5) cannot be 3 since the cell (R1,C5) in the same column C5 is 3. As a result, the cell (R5,C5) must be 4, as it turns out to be the only candidate left for the cell.
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The cell (R4,C5) cannot be 4 since the cell (R5,C5) in the same column C5 is 4.
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In the second case, suppose that the cell (R4,C4) is 4.
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The cell (R4,C5) cannot be 4 since the cell (R4,C4) in the same row R4 is 4.
As we can see in both cases, the cell (R4,C5) cannot be 4. We can conclude that the candidate digit 4 in cell (R4,C5) 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: Forcing Chain (candidate confirmed)