Dec 13 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R2C4 is the only square in row 2 that can be <4>
R3C3 is the only square in row 3 that can be <5>
R5C5 is the only square in row 5 that can be <4>
R4C8 is the only square in row 4 that can be <4>
R6C5 is the only square in row 6 that can be <5>
R8C7 is the only square in row 8 that can be <5>
R4C5 is the only square in column 5 that can be <6>
R4C6 is the only square in row 4 that can be <8>
R2C6 can only be <1>
R3C7 is the only square in column 7 that can be <1>
R3C5 is the only square in row 3 that can be <2>
R1C5 can only be <8>
R1C9 is the only square in row 1 that can be <2>
R7C7 is the only square in row 7 that can be <2>
R1C8 is the only square in column 8 that can be <9>
R2C9 is the only square in block 3 that can be <3>
Squares R6C4 and R8C4 in column 4 form a simple naked pair. These 2 squares both contain the 2 possibilities <27>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R5C4 - removing <7> from <179> leaving <19>
Squares R7C5 and R9C5 in block 8 form a simple naked pair. These 2 squares both contain the 2 possibilities <13>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R8C6 - removing <3> from <237> leaving <27>
Squares R8C4 and R8C6 in row 8 form a simple naked pair. These 2 squares both contain the 2 possibilities <27>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R8C9 - removing <7> from <678> leaving <68>
Intersection of row 8 with block 7. The value <3> only appears in one or more of squares R8C1, R8C2 and R8C3 of row 8. These squares are the ones that intersect with block 7. Thus, the other (non-intersecting) squares of block 7 cannot contain this value.
R7C2 - removing <3> from <1367> leaving <167>
R7C3 - removing <3> from <136> leaving <16>
R9C1 - removing <3> from <1389> leaving <189>
R9C2 - removing <3> from <13789> leaving <1789>
Squares R3C2 and R3C8 in row 3 and R6C2 and R6C8 in row 6 form a Simple X-Wing pattern on possibility <6>. All other instances of this possibility in columns 2 and 8 can be removed.
R7C2 - removing <6> from <167> leaving <17>
R7C8 - removing <6> from <367> leaving <37>
R7C3 is the only square in row 7 that can be <6>
R2C3 can only be <9>
R8C3 can only be <3>
R8C1 can only be <8>
R5C3 can only be <1>
R5C4 can only be <9>
R4C2 can only be <9>
R4C4 can only be <1>
R8C9 can only be <6>
R2C1 can only be <6>
R2C7 can only be <8>
R5C1 can only be <3>
R3C2 can only be <8>
R5C7 can only be <6>
R3C8 can only be <6>
R6C8 can only be <7>
R5C6 can only be <7>
R1C1 can only be <1>
R6C2 can only be <6>
R5C9 can only be <8>
R8C6 can only be <2>
R6C4 can only be <2>
R9C9 can only be <7>
R6C6 can only be <3>
R8C4 can only be <7>
R7C8 can only be <3>
R7C5 can only be <1>
R9C8 can only be <8>
R9C2 can only be <1>
R1C2 can only be <3>
R9C1 can only be <9>
R7C2 can only be <7>
R9C5 can only be <3>
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