Jan 01 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C4 can only be <7>
R5C3 can only be <9>
R7C2 can only be <4>
R7C5 can only be <5>
R3C5 can only be <2>
R1C6 can only be <9>
R5C5 can only be <7>
R6C1 can only be <5>
R6C5 can only be <9>
R4C1 can only be <4>
R4C5 can only be <8>
R4C4 is the only square in row 4 that can be <5>
R5C4 is the only square in row 5 that can be <4>
R6C6 is the only square in row 6 that can be <2>
R9C2 is the only square in row 9 that can be <2>
R1C8 is the only square in row 1 that can be <2>
R1C2 is the only square in row 1 that can be <5>
R3C2 can only be <7>
R2C3 is the only square in row 2 that can be <2>
Squares R9C4 and R9C6 in row 9 form a simple naked pair. These 2 squares both contain the 2 possibilities <36>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R9C1 - removing <6> from <168> leaving <18>
R9C8 - removing <36> from <1367> leaving <17>
R9C9 - removing <36> from <13678> leaving <178>
Squares R1C1 and R9C1 in column 1 form a simple naked pair. These 2 squares both contain the 2 possibilities <18>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R2C1 - removing <8> from <689> leaving <69>
R8C1 - removing <8> from <689> leaving <69>
Squares R5C7 and R7C7 in column 7 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 column.
R2C7 - removing <6> from <468> leaving <48>
R3C7 - removing <16> from <156> leaving <5>
R8C7 - removing <6> from <4568> leaving <458>
R8C8 is the only square in row 8 that can be <5>
R7C8 is the only square in column 8 that can be <3>
R8C3 is the only square in row 8 that can be <3>
Intersection of column 8 with block 3. The value <6> only appears in one or more of squares R1C8, R2C8 and R3C8 of column 8. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain this value.
R2C9 - removing <6> from <4678> leaving <478>
Squares R1C1 and R1C9 in row 1 and R9C1 and R9C9 in row 9 form a Simple X-Wing pattern on possibility <8>. All other instances of this possibility in columns 1 and 9 can be removed.
R2C9 - removing <8> from <478> leaving <47>
R8C9 - removing <8> from <468> leaving <46>
Squares R3C8 and R7C7 form a remote naked pair. <16> can be removed from any square that is common to their groups.
R9C8 - removing <1> from <17> leaving <7>
R2C8 can only be <6>
R2C1 can only be <9>
R3C8 can only be <1>
R3C3 can only be <6>
R1C9 can only be <8>
R1C1 can only be <1>
R9C9 can only be <1>
R2C7 can only be <4>
R2C2 can only be <8>
R8C1 can only be <6>
R8C2 can only be <9>
R2C9 can only be <7>
R8C7 can only be <8>
R7C3 can only be <1>
R7C7 can only be <6>
R9C1 can only be <8>
R5C7 can only be <1>
R8C9 can only be <4>
R4C9 can only be <3>
R4C6 can only be <1>
R6C9 can only be <6>
R5C6 can only be <6>
R6C4 can only be <3>
R9C6 can only be <3>
R9C4 can only be <6>
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