The logic of the Nishio technique is just like the "proof by contradiction" method in mathematics. Assume that an undetermined cell is the digit "k" say. If this assumption leads to a violation of the Sudoku rules, then we can confirm that this assumption is incorrect. As a result, this cell cannot be "k" and it can be removed from the cell as a candidate.
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In this puzzle, the cell (R3,C6) has two candidate digits. Assume that 3 is the digit for the cell (R3,C6).
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The cell (R3,C6) cannot be 5 since it is 3 by assumption.
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The cell (R3,C5) must be 5 since it is the only possible position for the digit 5 in row R3.
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The cell (R8,C5) cannot be 5 since the cell (R3,C5) in the same column C5 is 5.
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The cell (R2,C4) cannot be 3 since the cell (R3,C6) in the same block B2 is 3.
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The cell (R8,C4) must be 3 since it is the only possible position for the digit 3 in column C4.
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The cell (R8,C5) cannot be 3 since the cell (R8,C4) in the same row R8 is 3.
Now, we can see that there are no candidates left for the orange cell (R8,C5), and it cannot happen for a valid Sudoku puzzle. Therefore, we can conclude that the assumption that the cell (R3,C6) is 3 is incorrect. So the cell (R3,C6) cannot be 3, and the candidate digit 3 can be removed from the cell (R3,C6), as shown in Figure 8.
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