Dec 21 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C6 is the only square in row 1 that can be <3>
R7C5 is the only square in row 7 that can be <7>
R5C1 is the only square in row 5 that can be <7>
Squares R4C9, R5C7 and R5C9 in block 6 form a simple naked triplet. These 3 squares all contain the 3 possibilities <256>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R4C8 - removing <25> from <245> leaving <4>
R6C8 - removing <2> from <2349> leaving <349>
R6C9 - removing <26> from <2369> leaving <39>
Intersection of column 3 with block 1. The value <1> only appears in one or more of squares R1C3, R2C3 and R3C3 of column 3. These squares are the ones that intersect with block 1. Thus, the other (non-intersecting) squares of block 1 cannot contain this value.
R2C2 - removing <1> from <1256> leaving <256>
R3C2 - removing <1> from <1469> leaving <469>
Intersection of column 5 with block 2. The value <1> only appears in one or more of squares R1C5, R2C5 and R3C5 of column 5. These squares are the ones that intersect with block 2. Thus, the other (non-intersecting) squares of block 2 cannot contain this value.
R1C4 - removing <1> from <146> leaving <46>
R2C4 - removing <1> from <1678> leaving <678>
Squares R2C4 and R2C8 in row 2 and R8C4 and R8C8 in row 8 form a Simple X-Wing pattern on possibility <8>. All other instances of this possibility in columns 4 and 8 can be removed.
R3C8 - removing <8> from <89> leaving <9>
R7C8 - removing <8> from <589> leaving <59>
R9C4 - removing <8> from <458> leaving <45>
R6C8 can only be <3>
R7C8 can only be <5>
R6C9 can only be <9>
R7C9 can only be <8>
R8C8 can only be <2>
R8C7 can only be <9>
R2C8 can only be <8>
R8C6 can only be <4>
R9C7 can only be <1>
R9C9 can only be <3>
R8C2 can only be <5>
R9C4 can only be <5>
R9C3 can only be <4>
R8C4 can only be <8>
R8C3 can only be <3>
R9C5 can only be <2>
R9C6 can only be <9>
R5C5 can only be <4>
R9C1 can only be <8>
R1C5 can only be <1>
R3C5 can only be <8>
R1C1 is the only square in row 1 that can be <9>
R7C1 can only be <6>
R7C2 can only be <9>
R3C1 can only be <4>
R3C2 can only be <6>
R6C1 can only be <2>
R3C9 can only be <1>
R2C2 can only be <2>
R1C3 can only be <5>
R6C6 can only be <6>
R4C1 can only be <5>
R4C2 can only be <1>
R6C4 can only be <1>
R2C6 can only be <7>
R2C3 can only be <1>
R5C3 can only be <6>
R2C4 can only be <6>
R4C6 can only be <2>
R4C4 can only be <7>
R6C2 can only be <4>
R4C9 can only be <6>
R1C9 can only be <2>
R1C7 can only be <6>
R5C9 can only be <5>
R2C7 can only be <5>
R1C4 can only be <4>
R5C7 can only be <2>
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