Dec 12 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R3C4 can only be <5>
R4C5 can only be <6>
R6C5 can only be <1>
R7C6 can only be <8>
R7C4 can only be <4>
R5C5 can only be <9>
R8C4 can only be <9>
R3C6 can only be <2>
R8C6 can only be <6>
R2C4 can only be <1>
R9C5 can only be <3>
R7C5 can only be <5>
R3C7 can only be <3>
R2C6 can only be <9>
R3C8 can only be <7>
R3C5 can only be <8>
R1C5 can only be <7>
R1C3 can only be <2>
R1C7 can only be <9>
R1C9 can only be <5>
R7C3 can only be <7>
R1C1 can only be <8>
R2C8 can only be <2>
R2C9 can only be <6>
R2C2 can only be <7>
R2C1 can only be <5>
R8C8 is the only square in row 8 that can be <5>
R8C1 is the only square in row 8 that can be <1>
R9C9 is the only square in row 9 that can be <8>
R9C3 is the only square in row 9 that can be <9>
Squares R4C9 and R8C9 in column 9 form a simple naked pair. These 2 squares both contain the 2 possibilities <34>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R5C9 - removing <34> from <2347> leaving <27>
Squares R5C9 and R6C9 in block 6 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 block.
R5C7 - removing <2> from <124> leaving <14>
Intersection of column 1 with block 4. The values <37> only appears in one or more of squares R4C1, R5C1 and R6C1 of column 1. These squares are the ones that intersect with block 4. Thus, the other (non-intersecting) squares of block 4 cannot contain these values.
R5C2 - removing <3> from <2346> leaving <246>
Squares R4C1 and R8C2 form a remote naked pair. <34> can be removed from any square that is common to their groups.
R5C2 - removing <4> from <246> leaving <26>
R9C1 - removing <4> from <24> leaving <2>
R9C7 can only be <4>
R6C1 can only be <7>
R7C2 can only be <3>
R5C7 can only be <1>
R8C9 can only be <3>
R5C8 can only be <3>
R7C7 can only be <2>
R7C8 can only be <1>
R4C9 can only be <4>
R6C9 can only be <2>
R5C1 can only be <4>
R5C9 can only be <7>
R8C2 can only be <4>
R3C2 can only be <6>
R3C3 can only be <4>
R5C2 can only be <2>
R5C3 can only be <6>
R4C1 can only be <3>
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