Dec 08 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R3C1 can only be <6>
R5C1 can only be <7>
R7C1 can only be <9>
R3C8 is the only square in row 3 that can be <7>
R6C6 is the only square in row 6 that can be <7>
R8C7 is the only square in row 8 that can be <7>
R2C3 is the only square in column 3 that can be <2>
R1C3 is the only square in column 3 that can be <1>
R8C3 is the only square in column 3 that can be <5>
R3C5 is the only square in column 5 that can be <2>
Squares R2C2 and R3C2 in column 2 form a simple naked pair. These 2 squares both contain the 2 possibilities <35>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R4C2 - removing <3> from <3469> leaving <469>
R6C2 - removing <3> from <3689> leaving <689>
Squares R5C5 and R6C4 in block 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <16>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R4C4 - removing <6> from <256> leaving <25>
R4C6 - removing <6> from <256> leaving <25>
Intersection of column 3 with block 4. The values <34> only appears in one or more of squares R4C3, R5C3 and R6C3 of column 3. These squares are the ones that intersect with block 4. Thus, the other (non-intersecting) squares of block 4 cannot contain these values.
R4C2 - removing <4> from <469> leaving <69>
Squares R5C5 and R7C5 in column 5 and R5C9 and R7C9 in column 9 form a Simple X-Wing pattern on possibility <1>. All other instances of this possibility in rows 5 and 7 can be removed.
R7C4 - removing <1> from <1568> leaving <568>
R7C6 - removing <1> from <1568> leaving <568>
R7C8 - removing <1> from <1348> leaving <348>
Squares R5C3 and R5C7 in row 5 and R9C3 and R9C7 in row 9 form a Simple X-Wing pattern on possibility <8>. All other instances of this possibility in columns 3 and 7 can be removed.
R6C3 - removing <8> from <368> leaving <36>
R6C7 - removing <8> from <3689> leaving <369>
Squares R1C5 and R1C7 in row 1, R5C3, R5C5 and R5C7 in row 5 and R9C3 and R9C5 in row 9 form a Swordfish pattern on possibility <6>. All other instances of this possibility in columns 3, 5 and 7 can be removed.
R2C7 - removing <6> from <3456> leaving <345>
R4C3 - removing <6> from <346> leaving <34>
R4C7 - removing <6> from <3469> leaving <349>
R6C3 - removing <6> from <36> leaving <3>
R6C7 - removing <6> from <369> leaving <39>
R7C5 - removing <6> from <1356> leaving <135>
R6C7 can only be <9>
R4C3 can only be <4>
R4C7 can only be <3>
R4C8 can only be <6>
R9C7 can only be <8>
R4C2 can only be <9>
R9C3 can only be <6>
R5C7 can only be <4>
R5C9 can only be <1>
R2C7 can only be <5>
R5C5 can only be <6>
R6C8 can only be <8>
R6C2 can only be <6>
R9C5 can only be <3>
R5C3 can only be <8>
R2C2 can only be <3>
R1C7 can only be <6>
R1C5 can only be <5>
R6C4 can only be <1>
R7C5 can only be <1>
R3C6 can only be <8>
R2C8 can only be <4>
R3C2 can only be <5>
R2C4 can only be <6>
R7C8 can only be <3>
R8C8 can only be <1>
R3C9 can only be <3>
R3C4 can only be <4>
R7C9 can only be <4>
R8C6 can only be <2>
R7C2 can only be <8>
R8C4 can only be <8>
R4C6 can only be <5>
R2C6 can only be <1>
R4C4 can only be <2>
R7C6 can only be <6>
R7C4 can only be <5>
R8C2 can only be <4>
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