Jan 21 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R2C2 is the only square in row 2 that can be <2>
R2C6 is the only square in row 2 that can be <3>
R7C8 is the only square in row 7 that can be <6>
R7C3 is the only square in row 7 that can be <3>
R8C8 is the only square in row 8 that can be <3>
R1C1 is the only square in column 1 that can be <8>
R2C1 is the only square in column 1 that can be <1>
R7C1 is the only square in column 1 that can be <5>
R8C2 is the only square in column 2 that can be <8>
R6C6 is the only square in column 6 that can be <8>
R6C9 is the only square in row 6 that can be <2>
R3C9 is the only square in column 9 that can be <6>
R6C2 is the only square in block 4 that can be <6>
R6C5 can only be <7>
R6C1 can only be <9>
R5C5 can only be <1>
R5C9 is the only square in row 5 that can be <9>
R5C1 is the only square in row 5 that can be <7>
R4C1 can only be <4>
Squares R5C6 and R7C6 in column 6 form a simple naked pair. These 2 squares both contain the 2 possibilities <24>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R9C6 - removing <24> from <1245> leaving <15>
Intersection of column 9 with block 9. The value <4> only appears in one or more of squares R7C9, R8C9 and R9C9 of column 9. These squares are the ones that intersect with block 9. Thus, the other (non-intersecting) squares of block 9 cannot contain this value.
R9C8 - removing <4> from <489> leaving <89>
Squares R1C2<59>, R3C2<459> and R3C3<49> in block 1 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <459>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R1C3 - removing <9> from <679> leaving <67>
R2C3 - removing <49> from <4679> leaving <67>
R2C8 is the only square in row 2 that can be <4>
R4C8 is the only square in column 8 that can be <7>
R4C9 can only be <8>
R9C9 can only be <4>
R8C9 can only be <7>
Squares R8C5 and R8C7 in row 8 form a simple naked pair. These 2 squares both contain the 2 possibilities <59>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R8C3 - removing <9> from <149> leaving <14>
R8C4 - removing <59> from <1459> leaving <14>
Squares R2C5 and R2C7 in row 2 and R8C5 and R8C7 in row 8 form a Simple X-Wing pattern on possibility <9>. All other instances of this possibility in columns 5 and 7 can be removed.
R1C7 - removing <9> from <179> leaving <17>
R3C7 - removing <9> from <189> leaving <18>
R7C7 - removing <9> from <29> leaving <2>
R9C7 - removing <9> from <2589> leaving <258>
R7C6 can only be <4>
R7C2 can only be <9>
R5C6 can only be <2>
R8C4 can only be <1>
R8C3 can only be <4>
R9C6 can only be <5>
R9C7 can only be <8>
R1C6 can only be <1>
R8C5 can only be <9>
R9C8 can only be <9>
R3C7 can only be <1>
R9C3 can only be <1>
R9C4 can only be <2>
R3C8 can only be <8>
R8C7 can only be <5>
R1C7 can only be <7>
R1C3 can only be <6>
R2C7 can only be <9>
R2C5 can only be <6>
R5C4 can only be <4>
R1C2 can only be <5>
R3C3 can only be <9>
R3C2 can only be <4>
R1C4 can only be <9>
R2C3 can only be <7>
R3C4 can only be <5>
R4C5 can only be <5>
R4C4 can only be <6>
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