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Sudoku Puzzle

I just started with Sudoku and I jumped directly to a difficult level.

I have a hint but don't want to use it. Please provide logic with your answer.

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1 Answer 1

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Color your 48 cells with alternating colors. Any cell which sees both colors can be neither 4 nor 8. R3C6 sees both colors, so it must be a 5. enter image description here

The colors act as placeholders for the digits 4 and 8. You don't know which color is 4, and you don't know which color is 8, but any cell that sees both colors must see both digits and you can eliminate both digits from that cell.

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  • $\begingroup$ Sorry but I am not able to understand what you mean exactly $\endgroup$
    – Steve
    Commented Dec 30, 2023 at 7:42
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    $\begingroup$ @Steve That chain of 4/8 cells will be filled as 4-8-4-8 or 8-4-8-4, but the cell at R3C6 sees both ends of the chain so cannot be a 4 or 8. $\endgroup$ Commented Dec 30, 2023 at 8:33
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    $\begingroup$ @JaapScherphuis You should color R1C4 green. then you can show that the matching red in that square needs to be in R3C4 or R3C6. if you put it in R3C6 you will have two reds in C6 which is bad. So the red (the other matching 4,8) has to be in R3C4. This forces R3C6 to be 5 and the rest of the puzzle can be solved easily. $\endgroup$
    – DJ.
    Commented Jan 4 at 0:16

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